There are some microbes able to create single species ecosystems. So they should survive just fine introduced on their own to a new planet without life, if it is habitable for them.

This is one of them

Chroococcidiopsis - MicrobeWiki

It's a real survivor. Probably helped bring oxygen to our atmosphere. Doesn't need oxygen, can survive just fine in a CO2 atmosphere.

It can survive just about anything you throw at it, it's a polyextremophile. Including high levels of radiation,  fresh water, extremes of salinity, cold of Antarctica, heat of a hot spring, dessication in deserts. It doesn't need any other life to survive, just a bit of CO2, sunlight and rock and it's happy. It's also just fine in warm tropical seas or fresh water.

Leave it for a few million years on a planet with a CO2 atmosphere and you get oxygen in plenty.

But - note there are side effects. On Earth then when this microbe or others like it started to grow, they took all the CO2 out of the atmosphere, pretty much, which cooled down the planet. Luckily that's when our sun was getting hotter, so the end result was that the planet stayed much the same temperature.

So though some have suggested using this to introduce oxygen to Mars (Greening of the Red Planet), it only makes sense as part of a massive mega engineering scheme involving introducing greenhouse gases to Mars to keep it warm, or giant mirrors in space to double the amount of sunlight.  Because an Earth like atmosphere would not have nearly enough warming effect to keep Mars warm. Also humans can't breath a CO2 / oxygen atmosphere because CO2 is poisonous to us above 1% in the atmosphere, even if you have plenty of oxygen to breathe.

But you talked about a planet like Earth, not one like Mars. So - if you mean early Earth, so nitrogen, and CO2, but no oxygen- well this would help make it Earth like. But better not introduce it too soon or the planet might go into a deep freeze and maybe never recover.

Some people think that life automatically makes any planet more habitable for itself. If that was the case, just seed anything and it would become a more habitable planet for at least that type of life.

But - though there are many feedback cycles going on that do help to keep our climate stable, and Earth is certainly in a good place now in that respect, that's the weak Gaia hypothesis, I think there is plenty of reason to question the stronger hypothesis. There may also be a large element of luck. Perhaps sometimes life can be the agent for its own destruction too.

See Lucky Planet: Why Earth is Exceptional

In the case of Earth, I don't think it's necessarily the case that a "rewind" would end up in such a good place as it did. Might be that either the oceans boil away and it turns into a Venus - not something that can happen now but could have happened if it had never developed photosynthetic life, or if the photosynthesis that developed didn't create oxygen (we have several alternatives on Earth including the haloarchaea that turn the red sea read that don't produce anything much just act like our eyes do when we see light, use that as a source of energy - and other photosynthetic lifeforms that produce SO2 from H2S).

Or it might lead to a frozen Earth at least for a large part of its existence if it was introduced too soon, which might be the case if you introduced Chroococcidiopsis to Earth really early on.

So, you have to be careful terraforming planets :). Maybe if we study exoplanets with life on them, we can find out more and learn how it works for those.

It was also a very long process for Earth -  things like waiting for various lifeforms to evolve, billions of years, and slow changes from time to time over hundreds of millions of years. And you need to plan ahead also, if it's a young Earth think about what happens when the sun gets brighter, if it's an old one, what happens when it goes Red Giant etc.

You can speed it up probably with megatechnology or genetic engineering or whatever - but if you can do faster terraforming - what about faster accidental unterraforming? It seems to suggest more changes to go wrong as well as right.

See also my Trouble With Terraforming Mars

As for trying to recreate what happened on Earth - well we only have half the picture. Our understanding goes back to primitive DNA based life - but the smallest DNA based cell is just incredibly complex. DNA, translated to messenger RNA with a huge complex molecular machine with error correction, then that translated back to proteins,  using another complex molecular machine and translation table, and numerous other complex things going on in every single cell. Life can't have started like that. But we don't know how it started, and there's a big gap, lots of theories, but we are nowhere near being able to "evolve" our own new forms of life in the lab, can only tinker with the life we already have

So, we couldn't seed your planet with whatever was on early Earth because we don't know what that was, not yet anyway (perhaps we might find out on Mars or through early Earth meteorites on the Moon or in some other way). We have to seed with later lifeforms, which may or may not be suitable. (And even if we could seed with whatever came earlier, then who is to say that it would be a success the second time around after all the accidents of evolution that would follow?).

Basically we are too young and inexperienced a species to do stuff like this quite yet I think :).