Let me explain about going backwards. Buying investment property as an owner occupant provides superior lending terms such as lower down payment. You said you're approved for a 3% down loan versus if you purchased non-owner occupied you'd be looking at 20% down. This is because of risk to the lender. If times get tough will you make the mortgage payment on your residence before you make the payment on your investment property? People claim they will occupy to get the better loan terms, but sometimes they never do. The benefits of occupancy have been abused and lenders have cracked down on this.
Let's say you own a single family home and you're married with two young children. Then let's say you try to get a loan on a 4 unit property as an owner occupant. This is a red flag to the lender. They're going to be skeptical that you'll move your family into that 4 unit. That's a more clear example of going backwards. In this case buying the single family home eliminates the possibility of house hacking a multifamily. So find a lender who knows what they're doing, tell them your plan is to acquire more than one property over time as an owner occupant, and let them coach you on how to do it in such a way you don't disqualify yourself.
As far as hoarding cash, yes...absolutely. Why put down 5% on the first property when you're approved for 3? Save that. Your monthly cash flow, save that. What you would have paid for rent, save that. Have a fund ready for repairs and vacancies. Have the cash ready to buy the next one after you meet the occupancy requirement.
I should have said for cash out refi you can probably only borrow 70%. In 1-2 years with a 30 year amortization you're only going to pay off 1.5-3% of your loan. That may not even cover closing costs of a cash out refi. Even if you add 20% value to the property in that short time you haven't built enough equity to get anything from a cash out refi. That's why you need to hoard cash and save up the down payment for the next one.