Renting out my house to house hack a multi-family

[Michael DeFilippo]

Hello. This is my first post aside from introduction. I assume I'm not the first person to think of this, but don't see an exact match anywhere. That said, I apologize if this is a duplicate topic. Anyway, here's what I'm thinking:

I bought a house in NJ just over a year ago. It's 3 bedroom, 1 1/2 bath in a nice lake community. Shortly after moving in my son was born and daycare came into the picture. Anyone who has put their kid in daycare can tell you this is almost like taking on another mortgage payment. We can afford to live in our home, pay all the bills and eat... but its paycheck to paycheck at this point. I looked for ways to improve our situation and inevitably landed on real estate investing. 

I can ramble on about thought process and plot development but I'll get right down to it. I think the best move for me is to "house hack" a multi-family home, and rent out our house.

The monthly mortgage on my house with taxes, insurance, pmi, etc come out to $2000 per month. Based on comps for the area it looks like my house could potentially rent for between $2100-$2300 per month. 

The tricky part as I see it is how to get a mortgage on the multi-family (probably FHA) before I can show any rental income from my house... since I kind of need to live in it until I can move into the multi-family. It feels like a chicken or egg scenario... can't do one without having the other. We don't have lots of money or high income to entice a bank to lend us a mortgage on another house without selling the first...which is an option but not my favorite one.

Does anyone out there have experience breaking into buy and hold investing this way? 

Advice would be seriously appreciated. Thanks!