Welcome, Ristiia! Yours is a thoughtful question that, as Olivant said, we've discussed many times here because it deserves the attention we're giving it.

Yes, I believe Sol really wanted a deal. He saw that Sonny was "hot for my deal. And you [Tom] know it's the right thing." The novel also states that Sonny wanted an operation of his own and was anxious "to get out from under the Don's thumb." Solozzo surely knew that, too.
And, although the Corleones would lose some of their police/political protection with Vito dead, others would remail loyal to the Corleones. Sol would need them to protect his fledgling business, at least until he and Barzini were strong enough to buy those who had defected.

The key for Solozzo was to avoid an all-out war. He knew the other families would not dare attack Vito. But Sol must have convinced them that since Sonny was hot for his deal, there would be no war.

He miscalculated in two big ways: first, he failed to kill Vito; second, even if he did kill Vito, there'd be no way Sonny would make a deal. If Sonny made a deal, he'd look like a traitor to his father. The caporegimes and many others in the Family would suspect that he actually conspired with Solozzo in his father's death. Sonny would be at war with his own Family..