Then going into the town and manually moving the Forest tile onto the food tile.
The game is obviously trying to tell that in order to rule with the insight of a Roman patrician, you're going to have get all those forests cut.
All kidding aside,
The game invariably automatically puts the new Citizen to work in an unroaded Forest and automatically uses up that's turn's tile intake with it's own automatic choice.
This definitely has annoyed me in corrupt cities. On the other hand in a capital with "emphasize production" marked "Yes", if it has enough surplus food, it's 3 or 4 before it grows, a capital town with 8 shields blue will produce 10 shields though, which I find convenient (and there exist other examples) for production. But, a popup would be nicer for sure than going back and clicking on my capital manually!
Lacking a popup after city growth, maybe there's a variant here that could be interesting... try to have as many builds complete on the same turn as when a city grows. To do that, I'll suggest pillaging any iron sources so that one could produce a warrior or two when some other build can't get timed to match growth.
I think if you set a city to wealth and then use the queue to build something else, wealth only happens for one turn, and then it switches to the other build? The build changing from wealth via the queue to something else doesn't create city popups like built units, right?
Maybe with a little foresight for the turn time for a city to grow it might work though. Like let's say you have a 10 shield capital that you will grow in 5 turns, and you have horses. So, set the city to wealth, then wealth in the queue (does wealth exist in the queue?), or I dare suggest A CATAPULT, then your horseman. Then you can zoom to the city the same turn it grows.
Though maybe it results in a lot of warriors which seems excessive. But, maybe they could get disbanded in other cities every so often.
But would you win such a game where you tried to match growth time and builds, when in doubt about how to set up a city?
I think such a game might result in a fair number explorers. But, explorers can be useful for spotting potential attacks from AIs, transferring shields from one city to another, pillaging, and exploring.