Is it permissible in Sharia to leave the engaged girl—to whom one does not feel attached—and return to propose to the first girl, whose family did not explicitly refuse but only delayed their response, knowing that both girls are religious and of good character?

Marriage is the most effective cure for love. However, since the first girl did not respond to your proposal, sever your relationship with her for fear of temptation. Perhaps Allah turning her away from you was better for you. As for the second girl whom you proposed to and who accepted, if she is religious and of good character, then seek Allah's guidance (perform Istikhara) regarding completing the marriage with her. If it is finalized, then be content with it. And if Allah turns you away from it, then that is better for you.