Index Match to populate a diary based on trainer availability

Hoping someone can help me with this. I suspect it is really easy but maybe I'm barking up the wrong tree.

In Sheet 1 I have a list of dates for courses. In sheet 2 I have a list of trainers and their availability date. I am trying to populate sheet 1 using a formula such as Index / Match to look at the list of trainers on sheet 2, match their availabitiy date with a date on Sheet 1 and autofill their initials there. My stumbling block is that there are two trainers available each day so need to populate the Trainer 0815 -1630 Columns with a name... there is no preference which one goes in each time slot.

I'm aware there are only two trainers per month so would probably be just as simple to type them in manually alongside their relevant date, but I want to use this as a learning excercise to try and understand better using formulas to populate cells.

Cheers

Wow that is one terrifying formula and probably overkill using a sledgehammer to crack an eggshell. However it gives me an opportunity to pick apart the formula to try and understand how it works.
Many thanks for your time and expertise.