I'm guessing - instead of memorizing "7*9=63" (and numerous other products), you memorize that the multiples of 9 are "9,18,27,36,45,54,63..." and the 7th one in that list is the one you want?
First, you just learn to count them fluently. After that, you already know all the anwers, which is a huge head start.
I would have her count up and down. So now, just to learn the counting series she also had to do a bunch of addition and subtraction too.
After she could count the series, she could actually guess many of the answers the first time through a set of flashcards. And it only took a couple repetitions to get them all right.
And then, if you forget one, you can landmark off of easier ones, likes 5s and 10s. Since you deeply understand that 6x6 is just one more 6 past 5x6, you go 30+6.
It was fun and cute to see her working out the answers when she didn't know it off the top. And even if you have to count from 0, you're quick at it so it's not a big deal.
I am generally very good at taking tests but that was learned behavior. My origin story was a conversation about timed math tests with multiplication tables, and I was hit with the twin observations that you don’t have to do the answers in order, and if you can’t recall 7x9 but you can recall 9x7 it’s the same answer.
All of a sudden I wanted to know what other tricks there were and boy did I look for all of them.