The last new car I bought I did just that. I got a $3000 extra discount for financing then turned around and paid the loan off on the beginning of the third month.
After someone totaled that very vehicle in a parking lot while I was shopping I went out and bought my first-ever used car and have been very happy with it.
We are retiring soon and if we can take back our country I will buy both of us one more new vehicle and will probably have to do the early loan payoff to get a decent deal. If we need anything after that it will be used.
Did you finance through the dealer or separate bank/financial institution on your own?