Daniel went in - perhaps not in person, but by the mediation of some courtier who had access to the king. His first direct interview seems to have been Dan 2:25 [Barnes].
time - The king granted “time” to Daniel, though he would not do so to the Chaldeans because they betrayed their lying purpose by requiring him to tell the dream, which Daniel did not. Providence doubtless influenced his mind, already favorable (Dan 1:19, Dan 1:20), to show special favor to Daniel.