Your question is related to a very popular topic which is email list building. This is an area where maximum marketers strugle at the start. It is because building a big and responsive email list is not straight forward.
Customers are getting skeptic every day. They take maximum 5 seconds to judge a landing page or to connect with it. It could be even 2 seconds. So thats all you have to convince the visitor to opt-in.
Now I could have helped you better if I could see your landing page. But here are some times which you may help you-
1: Asses the visual appearance of your landing page. Is it connecting or appealing to your audience? Or its just a random landing page having few contents and a subscription box.
2: The headline, sub headline and subscription box copies. Are they creating hype, expectations, interest to the visitor? Without hype or interest, visitors wont opt-in
3: Are you delivering what you promised on the landing page? if so how long you are taking? are you emailing them with bribe contents or giving a discount or it is for newsletters?
4: Are you driving traffic to your landing page only from social media? If so does the landing page matches to the click channel like post on social media or whatever you are using?
Not having a domain restricts you to drive traffic from various places. But having a landing page should generate you some good amount of leads too. But if it is not optimized in terms of appearance, visuals, contents and forms it wont help.
Share your landing page URL. I think I will be able to help you further.