Domain Name - Trademark Question

Hello, I have been developing a concept for a website for a long time, and recently decided to purchase the domain for it. Unforuntately, the domain name i ideally wanted was already taken, however the site of that ideal domain was not ostensibly in use, and it only directed to an ad page. Therefore I decided to add a hyphen to separate some words in the domain. Now that I'm all established with the site online and trying to promote it publicly, I discovered through Social Media that the owner of that ideally named site is now attempting to begin using their site with the same name. I had contacted the site questioning if they were willing to sell the domain. It was not clear that they were planning on using the site as it was not working. Do I have the ability to claim that the trademark is mine? Can I file for a trademark if I was first to put my site online, and they tried starting it up after, even though they owned the domain before me?