Me, too, at least in the film. I blush to admit that it's been a while--a long while--but my memory is that we see him sorting through his mail, he finds the post card, and he walks across the street to the phone booth.
But it's been a while. ...
Certainly this is the impression left by the movie. I've just checked Striped Wall and one other site and the sequence of shots goes as follows:
1. Shot of "deceased" postcard.
2. Shot of phone ringing in Lureen's house.
3. Shot of Lureen answering the phone.
4. Shot of Ennis in phone booth with phone to his ear.
I can see that theoretically you can insert a time gap of whatever length you want between shot 1 and shot 2. However, that's not how the patterning of those shots come over to me.
As well, if Ennis is in a state of denial, then he would want that denial confirmed as soon as possible by hearing Jack's voice at the end of the line.
Quite how Ennis knows Jack's number in Texas is another - somewhat frivolous - question. Maybe, like Jack, it's something he kept in his head.