Lump sum principal pay-down to lower total effective interest rate?

I have been thinking about this for a while and was hoping someone smarter than me had any insights on this.

Let’s say I want to buy a home based on these factors: - $1,000,000 Purchase - $400,000 Down Payment - 7% Interest - 30 Year Fixed - P&I: 3,991.81

Total Interest Paid: $837,053.39

Could I instead lower my down payment to 20%, and on Month 2 make an additional 20% lump sum payment?

My thinking is that this would lock in a higher P&I payment and instantly accelerate my amortization and ultimately pay less interest + reduce my loan term (and worst case scenario if payment becomes too much can’t I request a loan recast?)

• New P&I: 5,322.42

Total Interest Paid: $387,545.84 Term Length: 15 years, 6 months

I was running some numbers and theoretically in this scenario the effective rate would be around 3.625% (in the sense that if I was able to get a 3.625% 30 year fixed putting 40% down, the total interest paid is about the same)

Is this possible??

TLDR; I want to make a large principal payment to lower my overall interest. Is it possible?