This is why I always work at a new company at least 6-12 months before making any major changes. I use that time to get into the flow of how things are being done (even if I think they are not efficient). I may make some suggestions but that's it. Of course, I'll probably never get hired again anywhere so it doesn't matter anymore.
In 6-12 months you could ship a new product or a large feature. This strategy might actually put you on a performance improvement plan instead.
That's why I said I'd suggest things. And of course I'd go along with strategic plans. Every company is different -- you'd be surprised at how many shitty [small] companies are out there that are actually profitable and want to keep things the same, refusing to do anything differently.