As I understand it, the Red Army had surrounded Berlin in late April and Hitler basically admitted defeat around April 22nd when Felix Steiner was unable to counter-attack. That time period seems to suggest a solid week between when Hitler basically gave up and when he killed himself.
Why didn't he attempt to flee Berlin? If the Red Army didn't get to his bunker until May 2nd, it seems that there would have been ample time for him to attempt escape. Were there no functional aircraft for him to fly out of Berlin? What was his motivation for remaining and eventually killing himself?
Mabye there would have been enough time to attempt to flee Berlin but there certainly wasn't a good chance to be sucessfull. Since we will never know for sure what Hitler thought there is not much sense in speculating about it. u/commiespaceinvader wrote an excellent op-ed about questions in the manner of "What did Hitler thought about....?".
German Historian Joachim Fest writes about the last days of the war and possible reasons for Hitlers suicide in his book 'Inside Hitlers Bunker' (OCLC Number: 52720633). Based on the recollection from Hitlers adjutants Heinz Linge and Otto Günsche, Joachim Fest comes to the conclusion that Hitler was shocked by Mussolinis execution on April 28th and the following abuse of his remains. According to Fest Hitler feared beeing treated in a similar fashion and wanted to avoid capture at all costs.
What we know for sure is that one day after Hitlers suicide Martin Bormann (NSDAP Party official close confidant of Hitler) and Ludwig Stumpfegger (Hitlers personal doctor) along with several others tried to escape from the Führerbunker and leave Berlin. Among them also was Hans Baur, Hitlers personal Pilot. They tried to escape on foot but failed and Bormann and Stumpfegger eventually committed suicide in the streets of Berlin. Baur was seriously wounded and became a Soviet PoW. To my knowledge, the only high party offical escaping Berlin from the Führerbunker in May 1945 was Artur Axmann (Leader of the Hitler Youth). He as arrested in December 1945 in the german city Lübeck.
Journalist P. O'Donnell claims Hans Baur offered to help Hitler escape by plane in late April 1945 but Hitler refused (from his book 'The Bunker'. OCLC Number: 1603646). O'Donnell based his book on several interviews with surving occupants of the Führerbunker. However his work remains controversial for several reasons (discussing them would go beyond the constraints of my answer).
In conclusion i hope i made clear that escaping from the Führerbunker (and the encircled city)in May 1945 was / would have been extremely difficult. There would have been a high risk of being captured and despite all speculation i think its reasonable to assume that Hitler would have tried to avoid that at all cost. Because the Allies had air superiority in Germany and Hans Baur diden't try to escape by plane himself after Hitler was dead i conclude that an escape in the air was not viable option.