Probably not in the way you imagine it happening.

First, you're probably not looking for open-ended critique. There are probably a limited number of things you're open to and capable of changing. They're probably mostly superficial things at best; you're probably not going to pay what it would actually cost for someone to analyze e.g. an onboarding flow.

Most designers deal with people who only want superficial changes all day long for their day jobs; they don't also do that for fun or beer money.

Second, a designer doesn't know anything about your users or your vertical. The most a designer could do is suggest things for you to test. You still have to build them out and test them.

If you're like most startups, you don't have infrastructure or traffic enough to do this well, to measure a baseline beforehand and change after the fact, etc.

Third, wherever you're located, there are probably local design meetups and professional chapters. They probably have happy hours and office hours. If you're really interested in improvement, you could follow my suggestions from this thread: https://news.ycombinator.com/item?id=8756258 pasted below:

Put together your customer lists. Make sure you understand their demographics and their usage patterns and why they purchased and what they were considering instead. Make sure you have ways to contact them for research interviews and if it's possible to go on-site to see them use your product live. Document how your competitors present and discuss their products.

Then, pick something. One small thing. A landing page. A particular form. A headline. Copy for a Google Adwords ad. Something you can measure your current performance on, and measure a change to afterwards. If you're not high-volume, this might be harder to find than you think, but go through the exercise of figuring out what you can collect enough data on now, and what can wait to change until you can measure it later (or what you don't care about measuring).

Then, you can take that one thing to a designer and say, "I'm looking to experiment with different changes to <X>. What are some things you think might be interesting to try? Anything goes."

You're not asking them to do any work. You're not asking them to stake their reputation on the line. Your language ("experiment," "different changes (plural)," "interesting," "try," "anything goes") all says you're willing to respect their time and level of engagement and also that you're prepared to handle their advice properly, that you're not looking for a silver bullet, you're looking for all of the lead bullets.

Say you ask for help with a landing page. A designer might suggest some copy or visual design tweaks for clarity (specific changes), but also suggest you test different headlines (without providing any), and also changing your format from short form to long form or vice versa (definitely without providing any content to you, but maybe they would be interested enough to sketch out some varied layouts). These are all great ideas. You should read up on A/B testing and test all of them in isolation, and also all together. You should test big dramatic changes even more frequently than you test small copy changes, because you don't want to be stuck looking for a local maximum. A UX person might also suggest ways to find out other things to test, research questions to ask, and suggest books or other resources so you can collect that data well.

A startup that came to office hours that well-prepared would basically almost not need design help at all.