Best growth hack: add a link to Google below your first results page. That way, more people will use your engine as their first choice, because they can easily fall back on their previously preferred search engine.
I can't emphasize the parent's comment enough. Being able to look through a set of results and then quickly get Google results if I don't find what I'm looking for are key to getting me to try any other search engine (For historical reference, this is how Excel killed Lotus 123 a few decades ago - by making it super easy to do Lotus exports from Excel so that people who tried Excel didn't feel like they were "trapped" into being outside of the Lotus 123 ecosystem at the time).
I saw the Google link you mentioned, but (at least on mobile) it didn't stand out. I would at least try doing a test where you put something super prominent up at the top of results: "Didn't find what you're looking for? Try your search on Google instead."