If a non-US SaaS company has sales in US, does it have to pay taxes in US?

Short answer is that you do not, unless you have presence, defined as nexus in the US.
You can read yourself in the many cases you are considered to have nexus from this source: https://www.webretailer.com/lean-commerce/us-sales-tax-ecommerce/
The definition is quite wide and varies between jurisdictions.

If your main business will be in the US, my advice is once you get high US traction, to get a local company in a low tax jurisdiction. Check Stripe Atlas for Delaware companies registration for a start: https://stripe.com/atlas

First you will have local presence and more trust, second you will avoid risking a drastic decision affecting international sales, which we all see can happen really fast these days.

My understanding of your business is that you are targeting the US as a market for your product. Questions that readily pop up based on the nature of your business are these- Do you have a business presence in the US? Or are you operating through agents? What Latin American countries are you operating from?

Business Presence in the US

If you do have a US business presence (like for instance operating through an office in the US, or registering an entity and having a registered address, or having one of your employees in the US marketing your products to US clients), you will find yourself generating US income which is subject to US tax. You also need to consider state taxes. In 2018, the Supreme Court decision in South Dakota v. Wayfair made it possible for many states to start claiming sales tax from remote sellers.
If you are operating through agents and they are not independent, that is as good as maintaining a physical presence.

Latin American Countries in Question

The country you are operating from is crucial because there could be bilateral tax agreements between that country and the US. So for instance, if you have no physical presence in the US, your customers will be obligated to withhold taxes on payments made to you. Bilateral tax agreements benefit you by reducing or even eliminating the amount that can be withheld from those payments.

As for your US clients, if they are for-profit businesses, they are entitled to deduct the payment for your services from their income.

My take

The answer to your question depends on your peculiar business model and how you operate, plus the nature of your interaction with the US. If you need further clarification, please feel free to call.