מדרש על ברכות 17:20

"the L-rd your G-d took you out of Egypt at night": Now did they leave at night? Did they not leave in the daytime, as it is written (Bamidbar 33:3) "On the morrow of the Pesach the children of Israel went out, etc."? We are hereby taught that the redemption began in the evening.

(Devarim 16:6) "But to the place that the L-rd your G-d chooses — there shall you sacrifice the Pesach offering in the evening, etc.": R. Eliezer says: Towards evening (of the fifteenth of Nissan) you sacrifice it. When the sun sets, you start eating it. At the time of your starting to leave Egypt, (i.e., at midnight) you burn (what is left of) it.