Thank you, and can I take the test in the Airport in TLV (or AMS) or I'd have to get it in town before leaving?
If your itinerary includes a connecting flight, your connection cannot be longer than 48 hours and travelers must present proof that their COVID-19 test was taken within 1 day of the initial flight departure.
You can buy a test kit in the US that you use via video conferencing / telehealth and they will send you test results which are valid for the US.
Airport in TLV only does PCR for outgoing which is expensive and unnecessary. You can find antigen in town in Israel for under 50ILS.
See
https://thepointsguy.com/news/at-home-covid-testing-travel/ for the test kits you can buy.