So, just to be clear, you want to start the 2015 historical season, but you want the Blue Jays' roster composition to be the one as of Aug 1st?
Do you want each team's roster to be as of that date, or are you primarily concerned with just Toronto's?
If it's just Toronto's, I'd start a historical game with 2015, and then look here...
https://www.retrosheet.org/boxesetc/2015/TM_TOR2015.htm ... and then manually make the changes that are dated after the start of the season and before Aug 1st.
If it's all teams, then you could do the same thing from here...
https://www.retrosheet.org/boxesetc/2015/YM_2015.htm ... but it'd be a significantly larger-scale endeavor. (And if it were me, I would ignore most of the transactions and only manually make the changes that are "significant.")
There may be some way you can run a test league to Aug 1st, 2015, export rosters, and then import them into your target league as of the start of the season. But I don't have any experience with this sort of thing and really have no clue if it's viable.
Good luck, though!