How can I determine the TAM and SAM of an SAAS company I am looking to startup?

Total Addressable (at least in the US) can be built based on market data sets, both free and for fee. For early child care centers, Market Data Retrieval and NCES (publicly available data set) are two recommended sources.
For Serviceable, that depends on a) your own business / operating model and b) the current and projected penetration of comparable competitors in market. For the former, consider things like technology usage and implementation capabilities. For the latter, if you have identified clear competitors, it is unlikely that you will have access to accurate info. So, if you can estimate these numbers and reverse-engineer, that's a good starting point. This would also be a great time to consider how your SAAS product is differentiated and will give you a chance to think through different scenario models for customer "switching" (from an existing competitor product to your own).

Post details of your system + likely others might provide unique perspectives related to your question...

Such as other markets you might access.

To an extent, your type of service will determine your TAM + SAM. For example, a pure software system can target every DCC (day care center) anywhere in the world.

If you have a hardware component, like webcams, then likely you'll have to only target your local area as you'll require installers.

Clarify your system + likely you'll receive some useful assistance.