Google did not become huge because of the search engine alone. AFAICT two things, based on related technologies, made Google oodles of money: AdWords and SERP ads. (AdWords used to be so unobtrusive I never tried to block them.)
I don't know how DDG currently pays its bills. They do feature unobtrusive and clearly marked ads on their SERP, too.
I'm not sure if ads can be reasonable without precise targeting, that is, tracking, tacit privacy invasion of various sorts, etc. Poorly targeted ads are disliked both by users ("dumb!") and advertisers ("poor conversion, money wasted").
The only other option I can see for a private company is to sell a subscription. Pay n USD / mo for no-tracking, no-strings-attached search.
The question is, of course, the value of n. It may turn out to be uncomfortably high for many users, just because advertisers value their eyeball rather highly.
You can already opt out of ads on some Google services, e.g. YouTube: try closing a few ads, or visit google.com/contributor when it (re-)opens. You can opt out of personalized ads, too. While many of us still won't trust all these measures, for many these would feel adequate.
I wish DDG all the luck. But being and staying an alternative, privacy-respecting search engine, even a low-profile one, isn't going to be easy.