In what moment I inject capital to the startup?

The other answers are good, and here is one practical approach to handling this.
First, the accounting capitalization (10m x $0.001 = $10k) is really irrelevant. In fact, we went for 10m x $0.0001 = $1k. Whatever you pick, your company after formation will show $X of assets (the cash in the back) and $X of shareholder equity. So far so good.
You then need to start spending money through the company. Rather than issue more shares, you can lend the money to the company; write out a loan agreement (probably something like a balloon payment 10 years out with 0% interest) and deposit the check.
If you're doing everything at the same time, and want to have $1k of shareholder equity with a total of $25k to spend, then deposit the $25k check and call it $1k to purchase the founder's shares and $24k loan.
In this case, your company now has $25,000 assets/cash, $24k liability (to you) and $1k shareholders equity: assets = liabilities + shareholder equity.
Hope that helps clarify things a bit...

So basically you are not correct. I think you need to gain a better understanding of the basics of capitalization. These should help:

http://www.axial.net/forum/business-valuation-intro-pre-post-money-valuation/

http://avc.com/2009/11/valuation-and-option-pool/

http://fundersandfounders.com/how-startup-valuation-works/

http://www.bothsidesofthetable.com/2010/07/22/want-to-know-how-vcs-calculate-valuation-differently-from-founders/

Those are good links that talk about valuation.

I think you are trying to make a link between the par value of the stock and the valuation of the business. There really is no link.

If you establish the corporation and are the only shareholder then you own 100% of the business. It doesn't matter how much money you have invested in the business. In fact, you don't actually have to put any money into the business.

This discussion of valuation only really matters when you want to bring in outside investors. and then, it still doesn't matter what the par value of the stock is, and it really doesn't matter how much you capital you have invested in the business either. What matters at that point is how much value you can convince an investor that the business is worth.

When it comes to finances, i'd suggest to not assume much. Financial discipline is imperative for any startup to succeed.
Following points would be helpful for you to begin with
1) keep a close watch on cash flow management
2) work lean and keep liabilities to a minimum
3) spend capital with a well defined measurement of ROI

You may want to check out the following course on Udemy

https://www.udemy.com/startup-launchpad-masterclass/?couponCode=MASTERCLASS

Also, you may want to schedule a call and i'd be happy to support further

You should inject capital in a start-up only when you have got optimistic answers to the following questions:
1. Is the team well-balanced, dedicated, and focused on the problem?
There are three parts to this question. When we talk about an early stage start-up team, we usually refer to the founders, plus maybe an engineer or salesperson. In most cases, investors prefer to see that these first team members have complementary skill sets and a similar motivation to solve the problem. The team should be able to clarify this information with their answer to the question, “Why did you start this business together?” Before we invest in a start-up, I also like to evaluate what this team looks like in practice. First, having at least two co-founders is ideal, and not just from an investment perspective. Our best investments often have at least one business founder (CEO) and one technical founder (CTO) to start, although we have seen successful examples that break this model. We also want to see that the entrepreneurs are working on their businesses full-time, which shows “skin in the game,” and that they have a strong motivation to solve a specific problem. A founder with a fallback will not chase profitability with the same hunger as an entrepreneur who cannot afford to fail.
2. Do the founders know their business, competitors, and industry?
We get hundreds of applications from start-ups in a wide range of industries, including pet commerce, last-mile delivery, and logistics. While these businesses might be good ideas or necessary for the region, they already have clear winners. For example, if we receive an application from a start-up that wants to compete with Colombia’s Rappi in the on-demand delivery space without mentioning this massive competitor, it is a red flag. Having competition or navigating a complex industry is part of founding a tech start-up. However, as investors, we would prefer to hear founders directly address these challenges. Rather than hiding the harsh facts, we rather ask for help in facing them. If an entrepreneur can explain their business in one or two sentences and their most significant threat to building it, then they are on the right track.
3. Is the valuation in line with the industry and the region?
We are valuation-sensitive investors because there have not been many high dollars exits in Latin America. Valuations can vary by industry, and more importantly, by region. Therefore, it is important that a start-up’s valuation is in line with similar companies in the same industry, city, or region. While exits and multiples are improving across Latin America, especially in Brazil, 2018 saw only a few $100M-$1B exits. The venture capital model does not work based on shaky returns. A high seed or A valuation can make it extremely hard for start-ups to raise future rounds or require them to do so at a down round. Asymmetrical valuation expectations can and do kill deals.
4. Why are they solving this problem?
The “Why” is often what motivates an investor to invest in a start-up. There are two main reasons for this fact:
1. Humans are naturally drawn to a great story. For example, people feel more motivated to back someone who is curing cancer to help their ailing sister than a wealthy founder looking to make a quick buck off the next Uber for Pets.
2. The “Why” is what keeps founders motivated when the going gets tough.
Every start-up reaches a moment when they need to pivot or change the model to solve the problem more efficiently. If the founders are more wedded to the “How” than the “Why,” then any pivot could kill the company.
5. Is the money machine working?
Once the team figures out how the company makes money, a strategic investment can be just what they need to take off. The money machine is working when a start-up has figured out how one dollar invested can turn into two dollars profit, or better. I am always impressed by entrepreneurs who have bootstrapped their businesses for years and prioritize profitability. A great example of this phenomenon is recent YC-grad from Colombia, UBits, which was bootstrapped (and profitable) for four years before raising capital. In the absence of a robust VC ecosystem, founders have to get the money machine working fast, or risk failing.
6. Is the company a fit for the VC fund?
Many investors laugh at the fact that investment theses are made to be broken. As an investor, I’ve ignored our thesis more than once in the heat of the moment. Only later did I go on to regret it. While our firm will invest outside of our thesis in the case of a killer company, the guidelines exist for a reason. If a start-up applies from outside our focus area, they should explain why our firm is the right fit to help them grow. Investors do not just create theses to have an excuse to reject start-ups. On the one hand, we base the thesis on which business models we think will be the most profitable or successful in the region where we invest. On the other, it also defines the industries where we believe we can be most helpful to entrepreneurs.
7. Does the start-up have an “unfair advantage”?
A fantastic idea, a solid business model, and a Rockstar team are all table stakes for receiving investment. However, what can make an investor take the leap is that secret sauce. It is the magic ingredient that will allow the company to “win” and dominate the market. Is the company already serving the largest client in the business? Does an industry titan back them? Did the founders sell a start-up or build something huge in the past that failed? A VC will want to know about it. In a sea of applications, these factors make a start-up stand out as a potential star. These are the start-ups to invest in and that could provide portfolio-defining returns. Start-up investment decisions are not as subjective as they seem. Every VC will have specific factors that motivate them to invest in start-ups. Most of all, I believe that start-ups should be so good that they (investors) cannot ignore you.

Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath

If you are a startup, you are always in fund-raising mode. As more investors come onboard, your "capitalization table" will change. Sophisticated investors don't like this 'cap table' to be messy (i.e., too many people at the party). Also, while raising funds, make sure, very sure you keep your legal and financial documents in order. Even if you have a winning product / value proposition, if these are not properly take care of, it's a big red flag.