Investing with the goal of paying off the house?

I know variations of this question get asked all the time but I feel like Im in a gray area. I know Dave would say extra cash at the house ... but curious was Dave minded folks think.

I owe ~500k on my home, recently got a new amazing job and should have an extra $5k a month to throw at the home if I stay gazelle intense with the budget(which I think I can for the foreseeable future). My ultimate goal is to pay off my mortgage, which is sitting at 3.375%. If I put an extra 5k a month towards the home I will clear it in 6.3 years ... if I invested in ETFs with the plan of pulling out and paying off when it crosses the magic number average returns of 10%,15%,20% it would be paid off in 5.5,5,4.7 years respectively. If the market returns 0% and we break even over that period it extends my payoff to 6.8 years.

I know the advice for saving for a downpayment is market if over 5 years and HYSA if under 5 years .... if my interest rate was higher I would just pay towards the house ... I want to mitigate risk but the potential of freeing up that money a year plus earlier makes me tempted to use the market. I am 34 if that factors in.

What would you do?