Hello! Welcome to Tumblr, haha. Here are some tips:
Be active. You can do this by posting regular updates, reblogging other people’s posts, liking things, and so forth.
Reblog. When I look at things on my dashboard, I sometimes look at where people reblog their posts from and check out that blog before following. Your followers will reblog from you and their followers will see where it was reblogged from.
Queue posts. Have a queue set up so your blog is regularly updated during the times you can’t make it online. It also invites people from different time zones to view your posts.
Have a nice theme. We can’t see another’s theme on the dashboard, but having a visually appealing theme does attract followers. Not only is it supposed to look good. It should be easy to navigate.
Tag your posts. People who then search something on Tumblr will be able to see your post. It also ensures your blog isn’t difficult to use as things can be found quicker.
Be nice. This is rather self-explanatory, I believe.
I’m really not that great of a person to ask since I might set a queue, but I won’t add more to it and it eventually runs out of things to post. Nevertheless, I hope you found the tips useful to some degree and good luck on your endeavours! :)