How to explain infinty to a $3^{rd}$ grader?

How to explain infinty to a $3^{rd}$ grader?

In my country in $4^{rd}$ grade in math kids learn the four basic
arithmetic operation (addition, subtraction, multiplication and divison)
up to $10 000$.
My sister this year goes to $3^{rd}$ grade and one day she was writing her
homework in math and out of a sudden she asked me up to which number a
know to add, subtract... I answered that I know to add, subtract... for
every number and because there are infinite amount of numbers, I know to
how to calculate up to infinity.
This concept of infinity was unclear to her. He couldn't go over the fact
that there are infinite amount of integers, because she thinks that
ultimately there must be a largest number, one that's bigger of all of
them.
I told her that because there are infinity amount of numbers I can always
say a greater number than one she can told. She start saying $600000,
1245000000, 99999999999$ and I easily just added $1$ and obviosuly that
makes my number bigger, but still it didn't helped her. I thought that
just adding $1$ to hers humber will make her feel that she's close to
beating me, so I though to double the number she says, but again it came
with no success, because she stubornly continued "fighting with
windmills".
How can I exlpain the existance of infinity to a 10 years old kid?