Athens airport wait time - due to new EES system?

We (family of 4) are flying from Athens to Dallas tomorrow (Sunday) afternoon. I got an email from American Airlines stating that we should arrive 3 hours early due to the new Entry / Exit System launched in April for non-EU nationals.

We are likely going to have carry ons only. How early do we need to arrive?

P.S. the carry on only plan may be foiled by a jar of capers that’s over the 100 mL. (180g). Do you think I should chance it ? The liquid in the jar is clearly less than the limit.