Time for wrist bands or hand stamps to be used at the doors.
IME, you better be there before the Gospel reading or no Eucharist with some exceptions.
If everyone falls into chronically being late, it will be pointed out and correction suggested.
When most show up "early", it is pointed out and with accompanying tones of gratitude.
Years ago, when I attended a Pan-Orthodox Retreat of Serbians, Greeks, Antiochians, and OCAers, the panel of priests instructed us that we had better be there in time for the Epistle
, or we should not partake of the Holy Gifts.
Furthermore, if one is nauseated, then one should not partake, no matter when one arrives.
However, this would be an ask your priest question
, as good parish priests do realize that young children sometimes have difficulty waking up. It is unwise to wake up a child and then have them scream in terror as they are still asleep. No one in their right mind would bring such a child in that condition into the church. It would be totally disruptive.
Nevertheless, it is better late than never.
There was this new parish priest, newly married, with no children. He was very strict about promptness.
Well, when he had his first two children, both of those young ones had trouble waking up. His Presbytera would either come late or not at all. They tried putting them to bed early, but that did not work. They tried everything. When their precious children reached the magical age of four, this problem mysteriously disappeared.