Well, the simplest way to answer your question will be a no. You cannot view private profile without following them. If you try to hack them or use any app to do so then instagram will surely ban you.
But there are some tips and tricks through which you can do so.
Following those person are the simplest way. But if you wanna watch the things they are posting then things will surely get difficult. Because you have chosen the difficult way.
If you know any mutual friend of the person whose account you want to visit without following them, then ask them whether they are following that person. If they do , then ask them to lend them their phone or whatever device they are using for visiting that person's account.
You can also use some Instagram bots which are available online to do this. But the bots which will give you the exact results will cost you money. There are some bots that are free to use. But most of them are fake and spam-my. So it's better not to use them.
You can try hacking there account. But for that you need skills and
enough practice if you don't want to get caught.
Deceive them. Pretend you are someone else, infiltrate that persons friends, then once you look like a legit account who is followed by that person’s friends, then send them a request to follow them and hope they accept.
You can also buy instagram comments, likes and followers for achieving this result too. If you boost your account by buying followers, likes and comments then the person you want to follow will end u following you first. Because you seem so popular.
But buy these stuffs from trusted sources. Otherwise, your account will face growth loss and lots of problems.
One of the sites who provide real followers and thus your content gets engagement. Promoting team is one of them. They are trusted too.
They give 100% guarantee to provide real comments and followers. As a result, you can instantly boost your credibility and get the required exposure for your business.
If they fail to provide comments and followers for any reason, they
guarantee your money back.
They are trusted too and a huge number of people use their services every day. So if you are interested then do give them a visit.
But cutting all these bullshits and wastage of time, the best way is to follow them. That’s it.