Ignoring it is worse case scenario^^
Also, i don't see the connect between depression and maturity. A mature person can become depressed, and vise versa. In theory a mature person can go through depression, and still retain their maturity. Even if slightly altered. Maturity is something way different from depression imo
Definition of mature is: "fully developed physically; full-grown."
Definition of depression is:
So if we are going with the literal definition, it doesn't make sense. However, if we're speaking "mentally mature" then it still doesn't make sense.
When you say "he's acting mature" or "he's always mature", it's generalized. No one can possibly have the mental strength to constantly have rational reasoning on the daily. It puts too much stress on the person, and will possibly lead them to depression because of it. That's why people snap, or rant, or anything of the sort. To take way some of the stress. Those actions then seem "uncharacteristic" or immature. Because it looks like it's not of rational reasoning, it's unorthrodox.
Same can go with getting out of depression. You can say "they were mature enough to get out of it", when in reality they could've gotten out if it sooner. You can't say "they gained the maturity to get out of it", everyone has the maturity to do anything. It just a matter of if they can mentally do that. Which is why there are professionals that help, have studied, and have evidence OF their study.
Everyone is mature, someone's level of maturity isn't static. It's constantly changing. Someone can be immature, yet still not be depressed. Saying maturity is related to depression doesn't make sense to me.