Quirky animation related question

I'm sure it's not the right title/question, but I'm facing an interesting challenge.

I've built and animated an actual bread factory for a client. Animation is composed of many loopable elements, based on a common global timeline for the most part. All client has to do is press play for it to start animating. Bread comes in and out of ovens, onto conveyor belts, onto palettes, etc.

The issue is, it takes 2 minutes for the factory to fill up with everything and looking like it's been looping forever. Client would like to have it already look full at play time. So, if we were to look at a traditional timeline in, for example, Premiere Pro, he wants everything to start at 0+10f.

Am I making much sense? Is such a thing actually achievable in Unity?

Thank your time and input!

A.