The Verdict: Clear Path
You are Mexican by birth, whatever your parents' nationality. Order a certified copy of your Mexican birth certificate, then apply for a CURP and a Mexican passport.
Mexico gives nationality to everyone born on its territory, or aboard a Mexican ship or aircraft, whoever their parents are. There is no residence condition and no other test.
You cannot lose it. A Mexican by birth cannot be deprived of their nationality, so holding another citizenship changes nothing.
If your birth was never registered in Mexico, that is common and fixable. Ask a Mexican consulate about late registration of a birth that took place in Mexico.
Your children born abroad are Mexican through you, and since a 2021 reform the line can continue to later generations.