Sometimes being first to market yields an unshakable dominance in that market for a long time to come... Mostly not though :)
What you're pointing out is often called 'second movers advantage'. Apples iPhone is a pretty decent example: by not being the first phone provider Apple got to enter a maturing market with a mature offering, use their own core competencies, and dominate. That's hard to do if you're bogged down with backwards compatibility and fighting to make the tech possible.
But for years they were basically just one among many sites, and not even terribly notable in the overall retail space. There were lots of other companies selling lots of other stuff at the time. Buy.com, for example, and ebay of course. Of all the ways to buy things online amazon was pretty far down the list until the mid 2000s.
What Amazon brought to the table was a unique combination of good web dev / services skills and top notch fulfillment logistics. And highly competitive pricing. Buying things on amazon was just a better overall experience compared to other sites. For example, when you put something in your shopping cart on amazon it stays there, it doesn't magically disappear for some artificial reason. And the overall experience of search/browse, read reviews, add to cart, then checkout, which today is commonplace throughout online retail was really particularly well honed by amazon. They didn't invent the form but they shaved off all the hard edges. This meant that amazon had much better customer retention than other sites and as amazon added new product lines existing amazon customers often decided to just use amazon for those things too. It took years and years for that momentum to snowball into the online retail juggernaut that Amazon is today.
A lot of other companies at the time had more revenue and invested more money into their stores than Amazon did, but they didn't win because ultimately they didn't execute as well. Amazon was helped by being online early, it gave them the experience necessary to build into what they became, but it's a stretch to claim they had first mover advantage.
That's just not true. Yes, they focused largely on books and music originally, but they were still a first mover in ecommerce and a huge presence. Heck, their 1 click patent was published in 99.
Lyft isn't a leap up from Uber. But I do stick with Lyft because Uber's been so cold.
Apple didn't sell the first smartphone or tablet...
Facebook wasn't the first social media site...
Amazon wasn't the first to sell shit online...
And Lyft wasn't the first ride-sharing app.
Maybe being first to market is overrated?