(This applies especially if you are trying to build a business, a brand or simply increasing engagement around your page. It could work better also if your page is about a single clear subject.)
My tip goes like this:
Give to others what you want them to give you.
Which means, if you want likes and subscribers, you gotta give those likes and subscribes to others ! Don't just stand there, waiting for people to finally find your content, go there and put yourself in front of their eyes !
What I like to do is using the tags exploration system. In my case, my Instagram page is about wood objects I create, therefore I'll choose the most generic hashtag representing the main subject of my page: #woodworking, and I'll browse the feed for this hashtag.
This feed will show you the latest posts with that hashtag, you gotta browse that feed, click "like" on everything that you appreciate, comment if you have something to say, check the page of the author, subscribe to them, etc ! The more you give to others here, the more likely they are to notice you and take a look at your page in return (out of curiosity or out of gratitude).
You might also get inspired by all the beautiful work others have put in front of you ! Sometimes it's refreshing to inhale the content of others, it gives you energy when it's time for you to exhale yours.
Good luck ! And why not put a link to your Instagram page in the comments below ? :)