@Joseph Fenner Joseph! I love the ambition. I wouldn't listen to people telling you it's unrealistic. Sounds like it's just unrealistic for them. Though, I would consider tweaking your goal. 167 properties at $500/month is $83,500 a year in cash flow and much easier to do on larger deals than aggregating smaller ones.
Instead of asking where you're going to find the money, I would be asking where you're going to find the deal(s). Further, your chances of hitting that cash flow number are much higher finding one or two great value-add apartment deals than it is finding 167 good cash-flowing single family homes (which is an oxymoron in my book...SFRs very rarely cash flow over long enough time horizons).
When I was a young multifamily broker, my goal was to broker enough to save up the money and buy deals to retire. I was told it was a 15-20 year goal because that's how long it took others. I found a fantastic deal in year 1, bought it on the 2 year anniversary of me stepping into the brokerage's doors, and that deal now pays my partner and I about $13,000/month each. It can be done, you just have to know how and where to look.
Action Steps:
1. Educate yourself on what a good deal looks like and how to structure the capital stack.
2. Figure out who would be the right partner in your market. This is tough and it takes time, but the big investors in your area would be tickled for a young/hungry guy to bring them a fantastic off-market deal, and would most likely give you free equity if the deal was good enough (I know I would).
3. Find the deal. Hunt for them. This takes a ton of time. Find the run-down apartment complexes in good areas. Forge relationships with the owners, and find authentic ways to create win-win scenarios in sale situations.
Is it easy? Nope. In fact, it's tremendously difficult. But the more difficult it is, the more money you can make.
Finding the deal is the hard part, not the money.