Can we change a theme after building a site?

Hello!

I have a website and i have been publishing a content and doing best practices of seo. 

Now, after all these years i never checked a site speed because i was just running google and facebook ads to generate sales. 

Now, i want to rank my website and get organic traffic. I have noticed that the site need more work to be done and the theme i was using does't worth it. 

That was a free theme. 

After knowing the SEO, I think theme should have these characteristics. 

1 - speed

2 - color scheme

3 - flexible

4 - seo ready

Now, will you let me know how to change the theme and make my site more flexible and more advanced. ?

Because if i will change the theme i will see phenomenal result. 

However, you can see the my site tennis ball machines for independent tennis player design here and recommend me the best theme to make my site superb and look professional. 

I need some professional reply here and guide me with there experience. 

Thank you .