You can't get a HELOC, to the best of my knowledge, without actually "owning" the house.
If you get an 80% mortgage (of the purchase price - not the appraised value, btw), you still need 20% as a down payment.
Once you own the home, you can apply for a HELOC ... presuming you have enough equity (eg, the purchase price is $40k less than the appraised value).
We haven't looked at the norm, at least where I live, of 5% down for a traditional mortgage and 3.5% for an FHA (which your question touches on).
If you can do 5% down, on a $1,000,000 mortgage you need $50,000 on the day of closing. If the home is worth (ie appraises for) $1,250,000, you're getting 20% of the house "for free". Presuming the bank(s) will go for it, you could likely then open a HELOC for as much as $250,000 (again, depending on individual lender rules).
If you don't have the money ready on the day of signing (via seasoning, if it is a loan/gift, or because you have been saving), you cannot afford the house.
To clarify from comments with the OP, I am in no way speaking to the buyer's ability to afford the monthly payments - this is only about affording the initial costs associated with the home buying process (down payment, closing, whatever else the bank(s) require, etc).