'In time' means to be ready before your enemy is ready. So I think the question you are really asking is why didn't the Russian army just keep going and arrive in France before Napoleon could raise and army. Why give him time to recover? So I will first answer the Russian side, and then some comments on the French side.

The Russian army retreat all the way from border to Moscow (500-600 miles), and then back all the way back to the border. And the Russian soldiers suffered not as much as the French soldiers did, but they still suffered quite a bit.

On the offensive they had to cross the same ground that the French had crossed and that already had been stripped of food the first time around. This offensive was very difficult and costly for them as well. Supporting the offense with the needed supply is difficult even in your own terrain. This means the Russian army that followed the French army was not some kind of steamroller that could just snowball from one victory to another like in video Specially when the next step of the operation was taking the offensive into enemy territory that was still defended.

Some Russian generals advised to not continue the offensive. There were important people in Russia who could already see that Britain was its longer term enemy as global empire. However Tsar Alexander and many others believed that Russian could not be safe specially if Germany remained in French control, Russia could never be safe. So the Russian army continued threw Poland and Eastern Europe all the way into Germany. However by that point they were an army exhausted from incredible distance covered and had to now face Napoleons new army.

To push into the German Heartland and even France, they had to raise many new units, just like Napoleon had to do as well. However the distance from the region where Russia assembled, trained and outfitted troops were further away from the front-lines then the French/German troops of Napoleon were. Consider the distance between Paris and Lützen (were a important Battle was fought) is 500 miles, the distance between Moscow and Lützen is 1000 miles. So it is not surprising why Napoleon had the upper hand at that point.

So this is primary what accounts for the fact that Napoleon basically reestablished numerical superiority very quickly. The Russian in Germany were at the end of supply lines going all the way back deep into Russia. Remember for example, much of the Russian horses came from the Eurasian Steppe. Had to be transported to somewhere in central Russia where Light Cavalry Units were trained and then transported to Germany. Napoleon had also left considerable forces behind that the Russians need to contain all across Eastern Europe. There were was considerable forces stationed in Eastern Europe and the Russian army had to make sure they didn't cause problems.

I think this answers the question better then talking about Napoleon. Napoleon controlled a very rich empire, with the best European farm land, good roads and a huge man-power reserve. The fighting would take place across productive areas of Germany that he controlled.

So, lets talk about Napoleons new army. Napoleon was able to pull large amounts of forces out of Spain. He pulled many Marines from the Navy as well. Add that to the already raised forces opposing the advancing Russian army. There were also the National Guard that he was able to move to Germany. These forces account for a army that matches the Russia/Prussia army.

Napoleon could call up more men too, with the same conscript raising system he had done before, if Napoleonic state was good at one thing, it was raising armies. They had reserves that were to be called up, the Russian campaign had not raised every possible solider and a year had passed with new young people turning the right age, he raised over 130k new recruits very quickly. Equipping these men was also not so hard as unlike in Russia, his land was not marched threw by a huge army, industry was intact. He had not yet lost political favor in Paris, there was no collapse of his government because of the failure of the Russian campaign. In fact, early on people didn't even know how badly the campaign had failed because Napoleon rushed ahead of the army. The finances of the French state were still miles better then those of the Russian state.

The far bigger issue for Napoleon, and something that he would never really figure out, was horses. The lose of horses, was devastating for him, he did not have the Eurasian steppe with massive amounts of horses and many highly skilled riders. Raising young men willing to fight is easier then horses. Training even a light cavalry unit was hugely difficult, and heavy cavalry was was several tiles more difficult then that. You have to grow and train the horse, you have to train the rider and then you have train the units.

Another problem for Napoleon was officers, the Grand Armee had consisted of lots of veteran officers and those of course take long to train as well (and preferable they have lots of experience too).

The army that he raised was still powerful and well lead overall. Some generals had to be jumped up bit more then they should. The moral of the soldiers was still good, most hadn't experience Russia, they mostly knew only about victory, even when there were many more young recruits then you would like. There was still a backbone of experience soldiers as well.

The army lacked large and experience cavalry forces. Light cavalry was a vital reconnaissance light cavalry and the Russians were known to have by far the best at that time. This means that Napoleon operated far more blindly then he had before, and couldn't exploit battle field victories in the same way.

Somebody else might be able to give more detail on the exact mechanism, institutions and laws used in Napoleon France to raise and train troupes.

tl:dr: Napoleon reserves, industry and powerbase was far closer to Germany, he could bring new forces far faster then Russian forces. He traded land for time, and he didn't need that much time.

Source:

Russia Against Napoleon: The True Story of the Campaigns of War and Peace

This is a great account of the whole story from Napoleon going into Russia all the way back to Russian marching threw Paris.