Seems like you have decent web development experience. I also agree that building an impressive Github profile will take a lot of time. You can always try on freelancing sites . If not, I do have one more suggestion.
1. Look for startups from Angellist or Crunchbase. Pick a couple of them based on your skills. Filter by remote working option. Also checkout https://remoteok.io/.
2. Once you have a couple of companies sorted, check out their blog and see if they have any public APIs available or not.
3. Build something with their public API. It doesn't have to be awesome. A simple working app is also fine.
4. Directly contact the company via Linkedin with your resume and show them the app you have built.
Overall the entire process won't take more than a couple of weeks. Clearing the tech interview is another thing. But I am sure you can get an interview with this approach. Hope it helps.
1. Look for startups from Angellist or Crunchbase. Pick a couple of them based on your skills. Filter by remote working option. Also checkout https://remoteok.io/.
2. Once you have a couple of companies sorted, check out their blog and see if they have any public APIs available or not.
3. Build something with their public API. It doesn't have to be awesome. A simple working app is also fine.
4. Directly contact the company via Linkedin with your resume and show them the app you have built.
Overall the entire process won't take more than a couple of weeks. Clearing the tech interview is another thing. But I am sure you can get an interview with this approach. Hope it helps.