I am eligible to claim interest from a HELOC used for home improvements but will not receive a 1098 because the interest is less than $600. How do I deduct the interest?

Just enter everything when prompted as though you have a 1098 Mortgage Interest Statement.  See Where do I enter my 1098 mortgage interest statement?

To read the entire TurboTax FAQ, click on What if I don’t have a 1098 mortgage interest statement?

The IRS lets you deduct your mortgage interest, but only if you itemize deductions. You can't deduct the principal (the borrowed money you're paying back). For additional requirements, see Can I deduct my mortgage?

I am being asked for my mortgage originate date

Enter the date you took out the loan.