Honestly, for me the early but not very early game (roughly years 20 to 60) is the most decisive part of the whole game. There's always peaceful jostling for territory with outpost races and so on, but also on appropriate difficulty settings, you will probably have to fight wars in this period (use Starnet AI mod if necessary) and they are some of the hardest wars in single player, precisely because you don't have very much stuff and haven't had time to outscale the AI.
If your neighbours are weaker militarily, you can go on the offensive instead, either full-blown or just enough to secure a decisive advantage over them going forward. If you don't want to do that, the thing to do is to invest heavily in tech, as many Researchers as you can afford (they'll mostly be on your homeworld at this stage). You're still "waiting for tech" but you won't have to wait very long, and the peaceful econ game is actually a lot more fun if you push a bit for the science/alloys/unity and keep spending your money, rather than just safely accumulating surpluses of everything. Once you are high-tech, you can transition into more offensive play (tech at this stage makes a huge difference to the power of your fleets, especially if you hit a good timing for carrier cruisers or you get battleships early), or you can use your superiority to expand your sphere of influence diplomatically. You'll also unlock Habitats relatively quickly, which will allow you to steadily increase your colony count without taking any more territory.
If you're playing on settings that are too easy for you, then of course the game will get boring. Stellaris is ultimately a strategy game, so it doesn't work so well played in chillout mode where you aren't challenged by other empires. You say you don't want to minmax but there are levels of minmaxing versus roleplaying. Generally I prefer to set myself some principles and goals (the roleplay aspect), forbid myself from using anything that seems like a cheese/exploit, but work strategically towards the goals within the range of "honourable" play. If done right, roleplay can actually enhance the strategic aspects rather than simply being "suboptimal", and conversely, having to think strategically gives the roleplay choices some concrete significance as opposed to just being pure vibes.
