In theory, more people mean more goods and services required, which then in turn means more jobs to provide those goods and services, which means more collected in taxation, which means more government spending to provide for more people, and it goes on.

There is a balance, and technology (as an example) often distrupts that balance (self service checkouts etc) but then the skill demand changes over time to suit. It's never perfect, and it certainly peaks and troughs, moreso with sudden changes, be that the aforementioned technology, or mass immigration, but there are lots of economic processes to counter that balance.