Could someone clarify how a cash out refinance would work after new construction.

Those are easy to finance, and the financing is solely based on the properties income using a DSCR ratio for qualification.I would look for a property like this one, https://www.zillow.com/homedetails/5810-21st-Ave-Kenosha-WI-...Lets say you could buy it for $100k, and its $50k in rehab, and ARV will be worth, $200k.When you do the rehab, make sure all the mechanical systems are brand new, then you will have relative few repairs for the next 3-5 years.I can get you a loan for $90k purchase, and $50k, rehab, once its finished you can refinance into a 30 year fixed rate loan between 6.5-6.8%, and cash flow. 

No question is stupid - its just not refined to get an educated answer.  

If you refinance keep in mind you can get up to 80% LTV even as an investment rental. 

If not, are there any that would allow us to refinance with no seasoning afterwards?

If you do not own a primary home its easier because you can claim any 2-4 unit as primary and only have to put down 3.5% for FHA, 5% for Fannie Mae or No money down 100% of you are a Military Veteran.Live in the home for 12 months refinance pull some cash out and move on to the next property to buy.

You'd need to look at how much this loan would cost you, how long it would take to recoup those costs...if you lock yourself in with a 5 year PPP and rates drop in 2 years, you're going to end up having to pay a hefty fee if rates drop and you decide to refinance.

I plan to regularly re-evaluate and refinance properties to pull out equity for further investments without over-leveraging.12.Professional Management: I’ll consider hiring a property management company to handle day-to-day operations, freeing up my time for further investments and strategic planning.Additional ConsiderationI've considered using the BRRRR method instead of paying off the mortgage first.

You could do a selective cash out refinance on one property to give you tax free living cash.If you do sell you'll want to do a 1031 exchange if you can so that you can avoid tax on all of your gain. 

@Kyle Weinapplehas the house gone up enough in value such that you could do a cash out refinance?