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Genesis 8:20
Then Noah built an altar to the LORD and took some of every clean animal and some of every clean bird and offered burnt offerings on the altar. (ESV)
How long afterward Noah landed did he make this sacrifice to God? He only had two of every kind of animal when he landed, so wouldn't sacrificing one of them render the species unable to propagate?
It is commonly assumed that Noah only took two (2) of every kind of animal into the ark. However, the scripture actually states that Noah took seven (7) of every clean animal and two (2) of every unclean animal into the ark.
In Gen. 7:2, it is written,
Of every clean beast, you shall take to yourself by seven, a male and his female; and of beasts that are not clean, by two, a male and his female.
מִכֹּל הַבְּהֵמָה הַטְּהוֹרָה תִּקַּח לְךָ שִׁבְעָה שִׁבְעָה אִישׁ וְאִשְׁתּוֹ וּמִן הַבְּהֵמָה אֲשֶׁר לֹא טְהֹרָה הִוא שְׁנַיִם אִישׁ וְאִשְׁתּוֹ
Therefore, Noah could have offered a sacrifice immediately since there was enough clean animals to continue propagating their own species after the sacrifice.
You are right - Noah took only two of each clean animal - see Genesis 6:19-20. This clearly includes cattle and all clean and unclean animals. This means he would make the entire species extinct if he slaughtered one animal before breeding took place.
But Noah also took seven of each clean animal and only two of each unclean animal - see Genesis 7:2. This means he could slaughter one animal without making the entire species extinct.
The reason for this is that there are actually two stories of Noah's Ark in Genesis 6-8, written by two different authors and cleverly interleaved so that the result appears to be just one, rather complicated story. The Redactor who edited the final version of Genesis no doubt felt that he would face opposition if he removed either one of the stories, so skilfully interleaved them so that the proponents of either story would find familiar text, yet the existence of two stories is not apparent.
The Flood verses attributed to the Priestly author are: Genesis 6:9-22, 7:6, 7:8-9, 7:11, 7:13-16a, 7:18-21, 7:24, 8:1-2a, 8:3b-5, 8:7, 8:13a, 8:14-19, 9:1-17.
The verses attributed to the Yahwist are: Genesis 6:5-8, 7:1-5, 7:7, 7:10, 7:12, 7:16b-17, 7:22-23, 8:2b-3a, 8:6, 8:8-12, 8:13b, 8:20-22.
The Yahwist reported that on leaving the Ark Noah built an altar and sacrificed one of each clean animal and each clean fowl. This was possible because the Yahwist was the author who reported that Noah took seven of each clean animal onto the Ark.
The earth was flooded for 150 years in that time the animals since they were male and female would have produced a first born (at least) since sacrifices and this was a Olah offering (burnt) the offering had to be of a certain age and clean. Noach would have sacrificed a first born male as a Olah offering.
Actually, Noah was commanded to take 2 PAIR of every unclean animal and 7 PAIR of every clean animal.
Then the LORD said to Noah, “Go into the ark, you and all your family, because I have found you righteous in this generation. 2You are to take with you seven pairs of a every kind of clean animal, a male and its mate; a pair of every kind of unclean animal, a male and its mate; 3and seven pairs of every kind of bird of the air, male and female, to preserve their offspring on the face of all the earth. 4For seven days from now I will send rain on the earth for forty days and forty nights, and I will wipe from the face of the earth every living thing I have made.”
Gen 7:1-4
Noah had plenty of clean animals to use as a sacrifice and still leave the various species well intact, especially if he only offered one male of every clean animal.
