Just admit to feeling it. Guarantee they're feeling awkward, if it's a first or second date, and they won't think less of you for feeling it too. Not having to pretend you're 100% comfortable can ease the stress quite a bit.
And, rather than focus on making a good impression, focus on getting to know this new person. For me, learning all about someone is fascinating and having that as my motivation, instead of worrying about making myself look good, also helps with the stress.
Plus, if you're trying to make yourself look good, most people can tell that's what you're doing. But if most of what you do is ask questions, and it's obvious you are genuinely interested, you'll usually make a good impression without even trying.
None of this will eliminate the awkwardness entirely, but it can reduce it to the point where your enjoyment level is higher than your stress level.
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If life's not beautiful without the pain,
well I'd just rather never ever even see beauty again.
Well as life gets longer, awful feels softer.
And it feels pretty soft to me.
Modest Mouse - The View