What are the best strategies to come up with the money for a first-time home buyer’s down payment?

I’m not sure there are any “best strategies”. I think you have to explore all the options, and come up with whichever one, or whichever combination, works for you.

The best strategy is to save your money.  After saving funds towards down payment and closing costs you can ask a Real Estate professionalto help you explorer down payment grants that could be available through your city, county, or state. Saving first is always the best strategy.