(Search for the Due on Sale clause in a mortgage and you'll see plenty of threads and opinions on that but it is very common practice).I would focus 99% of your time on finding the right area and property, as well as team - agent, Property Manager (@Stephen Glover is a very good start on this one btw), banker, Contractor, etc.

Would you still be living in the area and managing it yourself?

I would use your VA benefits, like @Jason Wray said, but use it for rental property purchase that you can learn to manage.

I had breakfast with another property manager, and we got to talking about the business. 

I didn't raise the rent after the first year as suggested by my property manager, who doesn't raise the rent on his great tenants.

Create a well-structured investment plan that includes your standards, target markets, property types, financing techniques, exit strategies, and risk management plans.

It’s the simplest way to get a feel of what it is like to be a landlord without going through the hassle of managing rehab projects.

I have reached out to a few property managers but to no avail.

In a past life, managing vendors for HUD, the following quote was a mantra we learned the hard way to live by:“People do what you inspect, not what you expect.”Louis V.

Key questions to ask include:Their experience with out-of-state investors.Knowledge of the rental market in Cypress, Katy, and Sugar Land.Experience with investment properties, particularly single-family rentals.Their network of local contacts, such as property managers, contractors, and inspectors, which can be invaluable for an out-of-state investor.Technology will be your ally if you are an investor from out of state.