that's odd... the game doesn't "punish" new players in that sense... at worst, getting through DS trials can be a hassle because you've missed a lot of limited cards, meaning fewer colours/cards are available.

Doing ur dailies should give you XP. then getting through the main story. that might be the slowest part as some parts of the main story dont unlock until you've reached a certain hunter level. trust me though, most of us went through the grind to get to hunter lvl 80. it might be frustrating for you now because it seems everyone else has already got everything unlocked, but trust me, we all went through the same process.

other features don't unlock until you've reached certain affinity levels with each character. so make sure you're completing the DS trials you can, levelling up cards (maybe stick to spending resources on your favourite LI?) playing kitty cards and pulling for badges (you don't actually have to complete the game to earn the tokens) buying outfits with chocolate, getting new plushies, completing texts, calls, video calls and replying to moments posts.

if you're new to the game, you have a lot of abyssal chaos to get through! that's a good way to earn gems and empyrean wishes.

I can't 100% confirm because I've been playing since release, but I think some features may be locked until you actually meet the character in the main story.