How to fill this gap between window and brick wall? (too deep for backer rod?)
If I were you I'd try this


Fill the gap with expanding foam. Give it a full day to cure (it expands so doing it too soon will potentially leave it uneven) and cut any bubbles off so it's flush
Buy some really good outdoor (oil based) caulk. The local big box sells something called Quad but if that's not available you can probably find something similar in grade. Caulk over the joint (1/2 inch is about the limit so be liberal). That will seal the window and protect the foam.