Let's not just dismiss the idea before we've even thought about it.
What is the use of this structure: we have even + past participle ( or present simple)?
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It means the same thing as:
Let's not just dismiss the idea when we have not even thought about it yet.
"Not even" in that context is a more emphatic usage with "not" (e.g. Cambridge)
For example "I didn't get out of bed on Friday" vs "I didn't even get out of bed on Friday" where 'even' is the emphasis. It gives the meaning that "getting out of bed" is a fairly minor thing, e.g. I was so tired... I didn't manage to do a small thing like getting out of bed and definitely didn't manage anything bigger!
So basically it means "let's not dismiss this idea before we've thought about it" but with the emphasis that 'thinking' about it would be the least amount of effort you could do.
Even is acting as an adverb here.
"We have even thought about it" is "we have thought about it" modified by the adverb even. "We even think about it" is "we think about it" modified similarly.
In such cases, it is function to indicate reality or an extreme example. It might be easier to approach in the negative first.
"Of course I haven't eaten dinner. I haven't even got home."
"I don't know what she'll want to do. I haven't even met her."
"We haven't finished that project. We haven't even started."
"I haven't found her. She's not even going to arrive for an hour."
These prototypical examples of "not even" show its most typical use, and the use comparable to your example. You would usually note that something "hasn't even" happened when confronted with the suggestion that some other thing might have happened that depends on the first thing happening first - you can't eat dinner before you get home, you don't usually know someone's preferences until after you've met them (though the internet makes that less true), you can't finish a project until you've started it, and you can't find someone who hasn't arrived where you're going to meet them.
"You can't dismiss an idea that you haven't even thought about."
That makes perfect sense, given the usage of "not even" illustrated above. It is also expressing the same general sentiment as your example. Your example might also be rephrased:
"Let's not dismiss the idea when we haven't even thought about it."
There are a lot of wider uses of the even adverb in this sense that don't map so easily to "haven't even", but your example does.