I don't know that there's anything quite as punchy, succinct, and general-purpose as "man-up" that doesn't have the sort of macho bullshit connotations, and if there is, it's probably some sort of psychobabble that wouldn't mean much to most people who need to hear it.

I'm also not a fan of the phrase itself, but the general sentiment represented by it has gotten me pretty far in life.

I'm not a religious person at all, but in certain contexts the "Prayer for Serenity" can kind of get you to a similar place.

For the SciFi nerds, there's Dune's Litany against Fear, or Yoda's "Do or do not, there is no 'try'"

There's also "mind over matter," you can't necessarily help what all the synapses and hormones and such in your body are making you feel, but you can sure as hell help what you do about it.

And of course from the advertising world there's Nike's "Just do it"

There's also some echoes of it in things like "be the change you want to see," or "if you want something done right you have to do it yourself," or "fake it til you make it"

Something else that has stuck with me is something one of my instructors said a lot when I was training to be a 911 dispatcher "don't do nothing." Make sure that whatever the problem is, you're taking positive steps to address it. You can't count on things resolving themselves, and you can't count on someone else fixing it either, you have to be the one to make things happen.

Again drawing from my own life experiences, I was a boy scout and the scout motto is to "be prepared" which I find pairs nicely with the saying that "people don't rise to the occasion, they fall to their level of training." Do what you can to prepare yourself beforehand, and everything will fall into place a lot easier when the time comes. That can mean physical or mental training and practice, or it could be something like getting your clothing, gear, tools, meal prep, cleaning materials together the night before and setting up alarms, reminders, notes, etc. to keep yourself on track.

For people inclined to read up on some philosophy, ancient Greek stoicism had a lot to say about things like self control and virtuous living, and daoism/taoism which has concepts like "Wu Wei" which is tricky to translate and keep the meaning intact, but it means something like "effortless action" it's kind of a mix of just doing what is needed as it comes up without having to think about it too much, and a bit of, like God said to Bender in Futurama "When you do things right, people won't be sure you've done anything at all."