The sacrifices in the old testament… approximately 2 million people bringing the priests sacrifices, were the priests sacrificing every day all day long?
There can be little doubt but that the priests were quite busy, and that many sacrifices were made. There are several mitigating factors to say that they were not overly busy. For one, the priestly family grew larger and larger as time went on. There were plenty of priests, and no shortage to keep the sacrifices going.
Then, realize that people were not necessarily bringing sacrifices constantly. There were three times in the year when every Israelite male (or every head of household?) had to appear before the Lord, and when he came, he could not come empty-handed, but had to bring a sacrifice. Yet they brought the sacrifice for their household. That means only every household had to bring a sacrifice, not every Israelite, so the number was somewhat smaller than it might have been otherwise.
Other than this, there were sacrifices that were going on constantly. There were daily sacrifices that had to be performed. Then, there were special sacrifices on the sabbath day, on feast days, and on the new moons (beginning of the month.) Besides this, there were sacrifices when a baby was born, sacrifices when one finished a Nazirite vow, and sacrifices when one committed a sin and was not aware of it. There were a considerable number of sacrifices. But remember that the high priest did not have to perform all the sacrifices, and so I think the large number of priests would have been plenty enough to perform all the sacrifices that were needed.
That said, when there were only Aaron and his two sons as priests, they probably were quite busy. No doubt they recruited Aaron’s grandsons to the task as soon as they were old enough.