How to form LLC w/ traditional financing and no proven history?

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Hi there. I'm a couple of weeks away from closing on my first SFR. I'm putting 20% down and getting a traditional 30 year fix under my personal name.

I'm getting umbrella insurance above & beyond my landlord insurance but am curious to hear from others on here how they may have gone about setting up an LLC for their investment property under similar scenario?

My understanding is that if the bank finds out you've set that up after you've already had a loan in your name, then it can trigger a due on sale clause....not a good outcome. Conversely, there's no chance I would have been able to get a mortgage under a new/unproven LLC. So I'm stuck.....

Does anyone know a way around this conundrum? Any advice for setting up an LLC even if you're new to REI?