Would that actually help slowly gather leads like I expect? or should I just focus on product and wait until I have sth to show for it
You can build a landing page. But I wouldn't let it distract you too much from the actual project, unless you are great at marketing, in which case, play to your strengths.
Understand that the title/lead/copy is very important here: I made a thing that I'm absolutely positive HN peeps would like, and it still took me several attempts at posting it (with various titles) before it caught on.