*naime from NAY?
eldamo.org - Eldamo : Primitive Elvish : NAY²

+Tamas Ferencz I consider NAY² to be a dubious root. It is a very late invention coined to explain nai “maybe”, which already has a perfectly good explanation as ná + i “may it be (that)”. It has no other derivatives and it also conflicts with the much better attested √NAY¹ “grief, lament”.

https://eldamo.org/content/words/word-2108335185.html

I think something based of KE/EKE might be better:

eldamo.org - Eldamo : Primitive Elvish : KE/EKE

Perhaps ecemë “chance, opportunity”

What would be a type of sentence where one would absolutely need a noun and could not express the same using the verb ek-?

+ܤܡܝ ܦܠܕܢܝܘܤ how about “I’m offering you a great opportunity”

+Paul Strack I am starting to warm to *ekeme, but would throw the variants éke, (e)kesse, ekesta, eque, ehta[1] into the mix
[1] using -ta as for '(one) result of action' = one instance of chance, opportunity

+Tamas Ferencz Of the above, I find ecesta appealing. The rest are (for me) to terse or obscure. egesta also has a decent Sindarin cognate: egest

entering *ekesta in the +#1000words list