edit: better link
350 was the level around 1990, which is thoroughly "after we already messed it up".
We can probably do higher; we probably don't want much lower.
Net zero emissions means a much higher level, just one which isn't constantly still going up.
I don't see how this is possible with our current population growth trajectory.
Instead of defining success based on climate stability itself, I think it makes more sense to define success in terms of what we care about: a thriving environment for humans and diverse other forms of life.
I think we'll be "winning" climate change, regardless of average temperature or CO2 level, as long as we're able to avoid catastrophic loss of human population and the rate of extinction is within some acceptable limit.
At the same time, the population has been booming to the point that close to half of the humans who ever existed are alive on Earth right now. This is a significant part of the current crisis actually.
https://www.prb.org/articles/how-many-people-have-ever-lived...
https://ourworldindata.org/future-population-growth
(Obviously, the error bars for a prediction like that are large.)
Many developed countries are already losing population:
https://www.worlddata.info/populationgrowth.php
An even larger fraction of developed countries would be losing population already if it wasn't for immigration. This suggests that as the developing world becomes more like the developed world, human population will be less of a concern for the global environment.
My perhaps radical position is that two best solutions for surviving climate change are birth control and education for women. The fewer people we need to keep alive, the more easily we'll be able to adapt to the changing climate.
I think it’s a bit late for what you are proposing however. Most of the world population is quite young.
[1]: https://www.co2levels.org/img/graph_grid.png
[2]: https://extension.okstate.edu/fact-sheets/images/greenhouse-...