Everyone seems to forget the bible wasn't written in English. The word "day" in the Genesis verses is Strong's #3117 in Hebrew meaning:
03117 yowm {yome}
from an unused root meaning to be hot; TWOT - 852; n m
AV - day 2008, time 64, chronicles + 01697 37, daily 44, ever 18,
year 14, continually 10, when 10, as 10, while 8, full 8 always 4, whole 4, alway 4, misc 44; 2287
1) day, time, year
1a) day (as opposed to night)
1b) day (24 hour period)
1b1) as defined by evening and morning in Genesis 1
1b2) as a division of time
1b2a) a working day, a day's journey
1c) days, lifetime (pl.)
1d) time, period (general)
1e) year
1f) temporal references
1f1) today
1f2) yesterday
1f3) tomorrow
As you can see, #3117 designates a time period, not exclusively a 24 hour period. The earth is billions of years old. Genesis explains creation. There's a lot of information in the first part of Genesis that doesn't immediately pop out, but will if you give your mind the key.
But, we do know that the record in the Hebrew text goes on to say that "the evening and the day were the first day." In fact, that same record is given for each day.
God created the foilage on the 3rd day, and the sun on the 4th day. He also told us that it was to reproduce after its own kind. This means that it was on its own. If there was a long period between those days, the plants and trees would have died, as they live by photosynthesis.
Really, it's simple. We make it more difficult when we add our own thoughts to fulfill our own thoughts and hopes.
It comes down to the fact that we were told that the evening and the day were the first day. That means that these were specified periods of time. It may be possible that the word can have different meanings, but when add the fact that the day was considered a combination of day and night, along with the fact that the plants needed the sun, that rules out your interpretation.