You have to tell the truth. Burden is on you to prove that you were in US on XYZ date and went on ABC date.
when you take flight from US the airline has your record
When you enter other country you get entry stamp on your passport and when you exit that country you may get exit stamp on passport.
When you take flight for US they know in advance that who is coming to US.
Airlines share data
The USCIS or CBP can find out anything about you if they want
You're supposed to be keeping accurate records (i.e. boarding passes) of all international travel as a LPR, especially if you plan to apply for citizenship when becoming eligible.
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