Yes, you should ALWAYS be first mover - but not in the way you may think. Microsoft frequently created or acquired products after other popular products were in the marketplace (example: Excel vs. Lotus 123), or as someone pointed out, MySpace to Facebook, and many many more.
But if you are selling to the same target audience as someone else, your product, the way you deliver it, the selling process, the location, price, or something else must be different than the incumbent and provide value that the incumbent does not.
Then you need to consider what the incumbent will do to compete and how fast-followers will try to out-value you. If you strategize that way and execute well, you will be able to stay ahead of competitors.
Consider Uber and Lyft. On the face of it, they provide the same service, but in reality the end-product is different and part of that is how they each interact with their drivers.