The coolest thing you can do right now in your situation is pause all your ads and devote 100% of your time for the next few days figuring out HOW to make tracking work.
Even if you think there’s no way, there is. And the highest value thing you can do for yourself and your client/employer is to figure out HOW to track accurately.
Use outside help if you need it. This one moment will reap rewards day in and out for the entirety of this ad account’s life.
Edit:
To add some value if for some unfortunate reason you absolutely cannot track conversions you can bid on manual cpc and just dial in your bids. Just understand you’ll have to track and most likely lose money each day until you figure out what the range of proper bidding for each day of the week.