When you say older I assume you mean pre-FE7 then? To be honest, not really. Fire Emblem 1 and 3 are very basic in their gameplay, so those wouldn’t be hard to play, but they’d feel like a step back from what you’re used to. The remakes help them feel more modern, but they only go so far (plus a lot of people dislike the graphics).
FE4 is pretty unforgiving (no trading, massive fights and map), but honestly I’d just try and dive into it. Personally I think it’s got amazingly fun gameplay, and I don’t remember it being terribly difficult early on, so you could probably ease into it. It’s really got its own thing going on, so you just need to try it out. It’s got marriage and a second generation, which should feel familiar to you as an Awakening player, so that’s something.
FE5… well, finish FE4 first, then move on to this.
Anyways, yeah, my advice is that if there’s a game you want to play you should just dive right in. Unless it’s FE5. If it’s FE5, play FE4 first, then you’re golden. For everything else, being comfortable with the GBA Fire Emblem games should give you a really solid base to move around on.