How do I start a cartoon animation company here in Cairo-Egypt?

There are sever steps on ding any company:
1st: Get the idea. You have this
2nd: You need to Register the company name. Think of the company name before hand with several options.
3rd: Make a bank account on the company's name
4th: Get a place of work: an office or a studio, paid or not
5th Hire the minimum staff.
6th: Start to work

The 2nd step is different in every country, you need to find what are the laws to let you legalize and register a company.

The 5th step is where I respond to your question:
Try to get a full time animator. You will need capital enough to pay this workers until the company get profit, but is very important that you have your own style, and for that you will need to have workers that have to implement that style

Starting an animation company in Egypt is similar to starting a company in any country. According to Wamda.com there are nine steps for Egypt specifically.

1: Trade Name Clearance Certificate (done by client).
2: Obtain a certificate from an authorized bank (done by client) .
3: Submit documents to the Companies Establishment Department, under GAFI (done by client).
4: Notarize company’s contract (done by client).
5: Obtain Chamber of Commerce Certificate (done by GAFI).
6: Issuance the notification of incorporation (done by GAFI).
7: Commercial Registry Certification (done by client).
8: Register for taxes (done by client).
9: Register employees with the National Authority of Social Insurance (done by client) .

Aside from the steps listed above you need to make sure you have a solid business plan with estimates of revenues and a clear explanation of your value proposition.

Reference: https://www.wamda.com/2011/05/how-to-register-a-company-in-egypt-the-complete-process

To start an animation company, the processes is somewhat same whether you are in Cairo or Copenhagen. Let us look at the steps one by one:
1. Start by identifying the kind of work you want to do: Ask yourself what kind of service you want to offer. If you are in the business of making short films, make sure you understand the full pipeline of animation production, from development through to pre-production, production, and post. You might think that this only really applies to big projects, but even small films need to go through the right processes, else they tend to get stuck.
2. Build your team: You may well not have all the skills needed to make short films. As an animator, you may want to team up with a designer (unless you are good at this yourself) and, if you are making 3D films, you will need expertise in modelling, rigging, texturing and lighting. By now you will be beginning to realise that to make short 3D films requires general expertise - this is where 3D generalists come into their own. Again, if you are making films, you will also need to appoint an editor, a director, a designer - and a producer to manage the process. The smaller the project, and the smaller the budget, the more likely it is you will need to wear some of all of these hats yourself. If you have enough general skills, you go can go into business alone. But remember the old proverb: "If you want to go fast, go alone. If you want to go far, go together".
3. Create a working name: Of course, your working name can simply be your name on the door. But a good business name helps people remember you and suggest that you might be more than just a one-man band. If your company name is a good one, you may will find that it helps you define what exactly it is that your business is setting out to do. As your plan grows, and things begin to take shape, the perfect name may come to you, but do not let that hinder you from getting started. You can always change it later. Create a name that you can use while you plan things out, and do not mind too much if you change it later.
4. Choose your team wisely: Be careful who you go into business with. Even your best friend may not be a great business partner.
Ask yourself if the other person complements your strengths and/or your weaknesses? Do both of you bring the same set of the same skills to the table? Ideally you want to be in business with someone with complementary skills to yourself. Overall, do you and your team see eye to eye on the big picture? Of course, there will always be arguments, but make sure you agree on the big picture, on the real purpose of your business.
5. Create a business plan: A business plan will help to define what you think you need to launch your business. Inside the business plan you (which could be a single page of A4) will summarise what it is that you are trying to do in a single document. In brief, your business plan should consist of the following elements:

1. The Business concepts. This describes the business, what the product is and who or what the market is for its products. What will be sold, who will buy it, and why is what you are offering better than the existing competition? If you are competing on price, how will you be cheaper than others?
2. Financial overview. Here you include the financial points of the business. What are your likely sales over the first year? What is the cost of doing business? Estimate the likely income and the likely expenses. Is it profit left over enough to make it all worthwhile?
3. Finance - requirements. This sets out what capital is needed to start the business, and to expand. If the business is just you and a laptop, you may not need any starting capital. If you need premises, you may need money to rent an office. This section should set out in detail how the capital will be used, and how much is required. Is the money being put in equity (ie a stake of the business, or is it a loan? If the latter, when will it be repaid, and on what terms
4. Define the company's legal status. This sets out all the relevant information about the company, its legal form of operation, when it was formed, and who are the principal owners and key personnel. Perhaps your business is just an informal grouping of friends? Or perhaps you want to set up a company or a partnership? Remember that someone will have to invoice clients, so a company bank account might be a good idea.
5. Goals and milestones. This sets out any developments within the company that are essential to the success of the business. Have you done any marketing, or tried to find out who exactly might want to buy your product? Are you looking to develop any new technology? Do you intend to open a physical presence in an office building? Are there any contracts that need to be in place?
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath