Typically the first purchase of the distressed properties do not qualify for traditional financing so investors use their own cash or heloc or private money to buy and rehab.

you can finance the first property many different ways. hard money, private money, heloc, personal cash, etc.you buy the property with that loan, and when you rehab you CREATE EQUITY, this is the crucial part you seem to be missing. so now you own a house for 75% of what it's worth.

Im in the middle of opening a Heloc on one of my investment properties with them and they have $0 closing costs... and even the appraisal is $0 charge regardless even if I decide to cancel the process after appraisal was done.  

I am 18 years old and living in San Francisco, looking to get into real estate investing.I have a ton of questions but some of the most nagging ones are the following:- Would it be easier as a young person with a lower income/credit history to buy a property cash, avoid any lenders, and then do a cash-out refi/HELOC after the purchase?

@Charles KaoSBA/CDC denied my underwriting for the 504 because the loan amount was too small and they didn’t like where my down payment was coming from (HELOC).

Willing to consider partnering with another investor but am also considering using a HELOC on my current primary residence to come up with remaining down payment.

To drop PMI and use a convetional you'll most likely need to finance at 80% LTV meaning the property will have to appraise at $421K (and you'll have to pay loan costs out of pocket). if you're living in the building your best option (imo) is to get a high LTV heloc. you don't have that much equity in the building yet it doesn't sound like but some HELOC loans go to 90% LTV (although be warned they will sandbag on the appraisal much harder) 

HELOC probably makes the most sense here.

If your interest rate is below the rates available today, I would consider getting a HELOC on your home.

You can also get a HELOC to get more equity out of the property, typically up to 90% but your rate will vary.