Hello
It sounds as though you and your co-teacher might benefit by asking the pastor or coordinator for some training support!
In the meantime however, if the two of you can sit down and decide on a lesson format that will be the same every week, and establish a time range for each part of your lesson, I think you will find it much easier going.

In terms of opening time, I am assuming you are meaning arrival time, as opposed to a "formal" opening time when all the kids are present?

Kindergarten children like routine, and knowing what to expect, so perhaps this arrival time can be used to help the children transition to the class room setting.

Word finds are beyond most kindergarten children, at least in the very beginning of the school year, but you could have some music playing as children arrive, and have tables set up with various activities that are more or less self-directed.

Puzzles are good, play-doh is good, and perhaps a bunch of scrap paper and materials for creating a collage of some sort.

You could ask the children to use the play doh or scrap materials to create something that God made that they saw when they came to church that day.

If you have someone available who could gather the children for a simple story, greeting, and a little conversation about how they are and how their week was, that is a really nice way to welcome children as they are arriving at different times.

This may be something that you could ask parents to do on a once a month basis, or once every two months, depending on how many children you have in your class.

This might be an especially nice option if you and your co-teacher are really needing that time to prepare and make sure you are ready for the lesson of the day.

Singing is a wonderful option, and you might want to see if there is a middle school or high school student who could come to the room and lead some singing time. Singing could be once or twice per month, and then have stories once or twice per month.

The other thing you did not mention was whether the children arriving up to 30 minutes early was really acceptable? Is the expectation that teachers/volunteers are in charge of supervising children for 30 minutes before and/or after the actual Sunday School time?

If that is not the expectation, then perhaps you can get some help in establishing clear arrival and pick up times.

I hope that helps, and that you and your co-teacher will soon have a great routine in place!

The beginning of the program year is always stressful~ hang in there!

Blessings
Jan S