Do the simplest thing that could possibly work

This is different from adding pointless complexity that doesn't help solve the problem but exists only because it is established 'best practice' or 'because Google does it that way' and I've seen this many more times than complex software where the complexity is actually required. And such needlessly complex software is also usually a source of countless day-to-day problems (if it makes its way out the door in the first place) while the 'simplistic' counterpart usually just hums along in the background without anybody noticing - and if there's a problem it's easy to fix because the codebase is simple and easy to understand by anybody looking into the problem. Of course after 20 years of such changes, the originally simple code base may also grow into a messy hairball, but at least it's still doing its thing.

If it doesn't, go from there whether you need to find an alternative or add another layer of complexity.

I think when complexity does build, it can snowball when a crew comes along and finds more than could be addressed in a year or two. People have to be realistic that there's more than one way to address it. For one it could be a project to identify and curtail existing excess complexity, another approach is to reduce the rate of additional complexity, maybe take it to the next level and completely inhibit any further excess, or any additional complexity of any kind at all. Ideally all of the above.

Things are so seldom ideal, and these are professionals ;)

No matter what, the most pressing requirement is to earnestly begin mastering the existing complexity to a pretty good extent before it could possibly be addressed by a neophyte. That's addressing it right there. Bull's-eye in fact.

Once a good amount of familiarity is established this could take months to a year(s) in such a situation. By this point a fairly accurate awareness of the actual degree of complexity/debt can be determined, but you can't be doing nothing this whole time. So you have naturally added at least some debt most likely, hopefully not a lot but now you've got a better handle on how it compares to what is already there. If you're really sharp the only complexity you may add is not excess at all but completely essential and you make sure of it.

Now if you keep carrying on you may find you have added some complexity that may be excess yourself, and by this time you may be in a situation where that excess is "insignificant" compared to what is already there, or even compared to what one misguided colleague or team might be routinely erecting on their own. You may even conclude that the only possible eventual outcome is to topple completely.

What you do about it is your own decision as much as it can be, and that's most often the way it is bound to always increase in most organizations, and never come down. So that's the most common way it's been addressed so far, as can be seen.