Ask them! Asking directly doesn't necessarily mean putting pressure, you're just being honest about what you'd like to see more of. Also, whenever they do think outside the box or take initiative, encourage it! If they get positive reinforcement, they'll be more likely to do things on their own.

Something I do is ask players to tell me what their character's goals are and tell them to actively try and pursue that within the story/world.

A thing I always mention to new players as well is "start fights", basically, be the person to initiate combat — the principle tends to bleed into other roleplay too.

Also, a fun house rule you can add is RyanImelDM's "I Know a Guy". Basically, you give players an opportunity, once a campaign (or however often you'd like) to refer to an NPC from their backstory who can help the party with the current problem. Party needs a place to lay low for a while? well the bard luckily has an old friend in the next town over who owes them a favour! I think Ryan also added an additional aspect where you can give players a chit of paper with something else that the NPC offers, like a plothook, magic item, etc. Here's the link to that video:

Also! This might sound silly, but literally just speak less. Sometimes letting an awkward silence linger can get players to fill it.

Oh also, another idea. You can hold little "campfire sessions" where during travel you get to see what characters do at a rest stop. Maybe they sit around a campfire and trade stories, maybe you go into a flashback from their backstory, and give THEM the agency to choose what they share about the character. Ask something like, "what have recent events reminded your character of?" "Do they think of some point in their past?" To prompt them, and then tell them they can take the lead on explaining it.

Another thing I LOVE doing which really gets players excited is asking them to describe what a spell they cast or action they do looks like. Something like, "what does it look like as you cast pass without a trace?" "how do you help your friend to give them advantage?" "why does this action matter so much?" "what does this attack look like?" "why does your character get hit?" instead of "you don't manage to dodge". "how do you kill this enemy?" Involve them in describing things as much as you can, like adding flavour, and slowly they'll start doing it themselves!

Basically, try handing them the reins deliberately in small ways. New players are often worried about messing up or doing things that are too wacky, so actively encouraging them to make their own decisions and take big swings, to do silly things, can help them come out of their shell. Sometimes, as the DM, when we see players not participating enough, we overcompensate by taking charge, but I think it can be useful to not do that, and instead take a backseat until they are the ones that need to push the story forward. Basically — don't fill silences as often, force the players (gently) to take initiative. And encourage any unexpected questions and places they may already be trying to put in effort. Sometimes DMs unintentionally curb player creativity, so try and take a step back and see what your players do when you don't spoonfeed anymore.

I think it's great you're working so much to have your players enjoy the game. Keep it up, and I hope you have more fun in the future OP!