The best and fastest way to get 1000+ visitors on your website is to make PPC campaign, so your site will be ranked on top of Google search result, the other option is to do backlinking for your site.
If you want drive move traffic to your site then you're going to have to think outside the box.
Find a well-known media outlet and get featured in one of the prime sessions of the website and you'll have many people being directed to your website.
Try that it works
Surprisingly, this is something that can be done provided you're willing to put in the work. You want 1000 visitors streaming to your website? Then promote your website to multiple places online and you'll get more people coming in to check it out. Think Facebook Ads, think SEO, think backlinks and press release etc. Some of these methods still work in 2019; however, the only determining factor will be the niche you're in.
Get good optimization. Or promote it to oblivion.
Link farming along with a very good SEO expert and you should be there in no time.
If you want to do SEO optimization of your site and gain more traffic to your new website, you'll have to research about long-tail keywords and write the content of your website for those selected keywords.
That way you'll not have much competition to face until you establish your website strong.
Link building is what you need to focus on next. Try visiting forums that are part of your niche and build your profile there and leave a link or two for your site on those forums.
It'll help in the long run.