Why were there no English subtitles provided during the conversation between Michael and Sollozzo?

A couple of reasons...

Firstly, Coppola states somewhere in the DVD commentary that the actors spoke too quickly for the subtitles to be read properly and that was a distraction for the audience, so he let the scene play out visually instead.

Walter Murch (Film & Sound Editor on The Godfather) explained why Coppola made this choice...

“It is very bold, even today, to have an extended scene between two main characters in an English-language film speaking another language with no translation. As a result you’re paying much more attention to how things are said and the body language being used, and you’re perceiving things in a very different way. You’re listening to the sound of the language, not the meaning.”

Secondly, although the scene is important, what Sollozzo is saying actually isn't.

The whole restaurant scene has very little to do the the negotiations but rather the killing of Sollozzo and McCluskey. This is the pivotal point where Michael makes his bones and sets off on the path of becoming the Godfather.

It doesn't really matter what Sollozo says, Michael is bound and determined to kill him (and McCluskey)...it all plays out in Pacino's expression and eyes...so, ultimately, the dialogue isn't relevant.

The audience also already knows what this meeting is about—Michael and Sollozzo are trying to reach a truce. That’s not what matters. What’s important is Michael’s emotional and psychological state. Because the dialogue is in a foreign language and therefore “unimportant,” we can focus our full attention on Pacino’s amazing performance. Pacino has to pull off a very difficult feat here—he must convey to the audience his nervousness and doubt while simultaneously conveying to the characters in the scene that nothing is out of the ordinary. The way that Michael glances down, the way his shoulders slightly sag, the frustration in his eyes when his Italian fails him—Pacino creates a subtly physical performance that brilliantly captures the character’s state without giving anything away to the other characters.

^Source