How do I check to see if the federal government got my payment? Not on my bank statement.

https://www.irs.gov/

use the view my account link. 

but considering the IRS may be shorthanded and thus slow in processing checks it may be a while before it posts.  you actually had til 7/15/2020 to make payment for balance due on '19 return. ist '20 estimate due 6/15/2020 

as a last resort call the iRS buy be prepared for a long hold time.