The feast was prepared during the daytime of what we would call Thursday. The first day of the feast of unleavened bread, otherwise called Passover, was Friday.
And the first day of unleavened bread, when they killed the passover,
his disciples said unto him, Where wilt thou that we go and prepare
that thou mayest eat the passover? (Mark 14:12, KJV)
The Greek verb translated here in the KJV as "killed" (it could be translated as "sacrificed") is in the imperfect active indicative tense, which indicates a past action, and it can also indicate an ongoing action. For example, if I speak of a past time in my life and say "I was eating vegetarian food" or "I ate vegetarian food," in English, both of these mean essentially the same thing: neither one requires that the action is happening at that very moment, merely that it is happening on an ongoing basis, as a habitual action.
So it is important not to overanalyze the translation to determine an exact time for when this occurred. The text already gives us the time as "the first day of unleavened bread." That is all we need to know.
The first day began at sunset. It continued throughout the following day, ending at sunset on what we call Friday (the preparation day for the Sabbath). It was during that day, Passover, that Jesus was crucified. So he ate the Passover meal with his disciples in the evening of the day, and during the "morning" of the same day, which follows evening, Biblically (see Genesis 1), Jesus died.
In John, the text is clear that when Judas went out, it was dark (night). That day would have started well before that when it was yet twilight--at sunset. However, it was before sunset that the disciples gathered in that room and made preparations for the evening meal.
Yes, Mark's account begins before sunset. But it was after sunset that their Passover meal was to begin.