Elias here with Shopify Support. Thanks for reaching out!
Though some third-party themes may come with a predictive or smart search bar, I can't be sure if Blockshop does. However, you can reach out to the theme developer and see if it's something they can implement. Blockshop is made by Troop Themes, you can contact them right over here.
There's also a few third-party apps that can integrate predictive search with your theme, they also include additional features that you can use with your store (eg. product filters). That being said, I've handpicked a couple of them for you to try out:
If you need any assistance with these apps, you can always reach out directly to the developers through the contact information found in the Support Section of their app's page.
I hope this gives you a couple of options to consider for predictive search. If you have any other questions on this topic, don't hesitate to let me know!