It sounds like you are proposing to do a Master Lease Option (MLO) agreement. Basically, you agree to take over management for a period of time with an option to purchase the property within at a previously agreed price. Do a search for that term to learn more about how they work. You would still need to negotiate terms that make this a good deal.
As a beginner in multi-family investing myself, I would be willing to take over management just for the practice as long as I don't bear any financial risk, even if I don't end up buying it.
If you did improve the NOI up to the mortgage payment, is there still room for improvement even further such that it would cash flow? If so, then the terms of your MLO could be such that you only pay the net until it equals the mortgage payment, but then you take any profits above the mortgage payments with an agreement to purchase the property subject to the existing loan. This of course is dependent on the mortgage balance being at or below the new market value, and that you can improve the NOI with minimal capital expenditure. Crunch the numbers to see if they make sense. This might be a good chance to purchase a property with no money down if you can make it cash flow. As I said, I am a beginner, so take it for what it is.