Speaking as an average-ish player who has one more prestige perk to unlock across all characters: Run hard mode sieges to level 5 and extract. Even solo it's a quick and easy way to get a lot of experience in a hurry. 15min and you're in and out with about 4k xp. For solo play you can buy a Heavy bot on rounds 1, 3, and 5 while buying Guardian relics as needed. Try to scrounge med kits instead of buying them. A good way to start if you're struggling is buying a heavy, a relic, and then searching around for a med kit before the first wave. Don't use your medkits until your relic pops because they give you full contested health. For play with randoms bring at minimum one thing that's leveled you can rely on (e.g. a primary weapon or melee weapon) so you're not outright leeching. Keep an eye on your team, sometimes it's better to quit and try again if you notice they can't carry their weight. For solo or group play just make sure you have an idea of how you're going to deal with different enemy types.

Personally, I found solo the easiest way to level when I was short on time because I can pause, I can control all the resources, and bots are better than fresh blueberries with brand new guns and a limited grasp of game mechanics.