At least in the Gemara it's clear that Achashverosh also wanted to get rid of the Jews and was happy with Haman's scheme. Megillah 14a commenting on Esther 3:11 says:
מָשָׁל דַּאֲחַשְׁוֵרוֹשׁ וְהָמָן לָמָּה הַדָּבָר דּוֹמֶה? לִשְׁנֵי בְּנֵי אָדָם, לְאֶחָד הָיָה לוֹ תֵּל בְּתוֹךְ שָׂדֵהוּ וּלְאֶחָד הָיָה לוֹ חָרִיץ בְּתוֹךְ שָׂדֵהוּ. בַּעַל חָרִיץ אָמַר: מִי יִתֵּן לִי תֵּל זֶה בְּדָמִים! בַּעַל הַתֵּל אָמַר: מִי יִתֵּן לִי חָרִיץ זֶה בְּדָמִים!
The actions of Ahasuerus and Haman can be understood with a parable; to what may they be compared? To two individuals, one of whom had a mound in the middle of his field and the other of whom had a ditch in the middle of his field, each one suffering from his own predicament. The owner of the ditch, noticing the other’s mound of dirt, said to himself: Who will give me this mound of dirt suitable for filling in my ditch; I would even be willing to pay for it with money, and the owner of the mound, noticing the other’s ditch, said to himself: Who will give me this ditch for money, so that I may use it to remove the mound of earth from my property? (Shteinzaltz translation and elaboration).
Also the gemara on 13b elaborates on what Haman said in 3:8-10, and those criticisms are clearly specific to the Jews. I.e., Haman was trying to incite the King against the Jews and not some vague undesirable nation.
As for Esther, Achashverosh did not know what nation Esther was. That's pshat in Ether 2:10, and mentioned repeatedly in Megillah 13-15.
So, based on the gemara, Achashverosh knew the decree was to kill the Jews but he did not know Esther was Jewish, so he was surprised by her revelation (especially since he was antisemitic so why would he think his wife was Jewish).
If you want a more "pshat" answer not based on the Gemara, Achashverosh didn't know the nation Haman had in mind but was shocked to find out it was the same nation as Esther. After all, he was king over 127 nations so the odds were less than 1%, and furthermore it seems quite audacious for Haman to go after the Queen's nation. Either way, to your specific question, there was no evidence for Achashverosh to "put together" until Esther's denouement.