Core teams can be of different types.
The early employees (the founding team basically) are usually very closely knit and they wouldn't want to talk things out but rather want to own it up by themselves and drive things forward. Sometimes if you joined a bit late, even a junior employee by grade but a founding team member can still choose not to open up to you or have you feel included because of the exclusivity they get to enjoy as a founding team.
The next type is if your core team is full of IIT/IIM folks who studied together or have worked together in the past and have a very strong bonding/networking benefit, it would be very difficult for you to crack through and have a seat at the table in this scenario too.
What I would suggest is your work being finished on time and exceeding targets is fine, but look at avenues where you can own up new tasks or bring initiatives across the growth funnel which was not even supposed to be yours in the first place. It can be belonging to a different team too but they may have completely skipped even looking into it. There will be resistance but that's the only way you garner visibility across the organisation and grow. I'm assuming it's a startup so you can always find a way to penetrate through things and fix them and it should be welcomed, assuming the culture is good.