How did 搭 + 訕 compound to mean 'strike up a conversation' or 'reply evasively'?
From Zdic (汉典), 搭 has also the meaning of &quot;to come into contact, to meet&quot;:


交接，配合：～配。～伙。～档。～售。～伴。～帮。～腔。～话。～界。～讪。


The last one in the above entry is exactly the example of 搭讪.
The same dictionary provides an entry for 讪 (but also MDGB does), where it's shown that 讪 alone means &quot;to mock, to ridicule&quot;.
So 搭讪 together is somewhat an extension of the two meanings of 搭 and 讪, like to meet a mocking (meet = counter). MDGB again gives &quot;to end an embarrassing silence by striking up a conversation&quot;, and Zdic &quot;勉强找话说以消除尴尬&quot;.

PS: I vividly suggest you include Zdic in your preferred vocabulary sources. Even though the interface is in Chinese, you can easily copy-paste characters in the search bar and get decent results.
PS 2: I'm not sure why you think that words composed of 2+ characters must absolutely reflect preexisting meanings of the single characters. Languages can be productive.