I've been trying to remember a short story which I read in the 1980s in a sci-fi anthology.
I recall a ship arriving an alien planet and watching as evolution from bacteria to fish, reptile, mammal, human, ...took only a couple of days. If I remember correctly, it ended with the creature that evolved after man. Does this ring a bell to anyone?
"Student Body", a novelette by F. L. Wallace, available at Project Gutenberg, also my answer to the old question Short story about human colonists vs. alien animals that evolve very rapidly. It doesn't start with bacteria, the progression of forms the "omnimals" take is squirrels, mice, rats, tigers, men. And we don't see what comes after men:
"Don't you still see? There is a progression. After the tiger, it bred this. If this evolution fails, if we shoot it down, what will it create next? This creature I think we can compete with. It's the one after this that I do not want to face."
It heard them. It raised its head and looked around. Slowly it edged away and backed toward a nearby grove.
The biologist stood up and called softly. The creature scurried in the trees and stopped just inside the shadows among them.
The two men laid down their rifles. Together they approached the grove, hands spread open to show they carried no weapons.
It came out to meet them. Naked, it had had no time to learn about clothing. Neither did it have weapons. It plucked a large white flower from a tree and extended this mutely in a sign of peace.
"I wonder what it's like," said Marin. "It seems adult, but can it be, all the way through? What's inside that body?
"I wonder what's in his head," Hafner said worriedly.
It looked very much like a man.
Might you be thinking of "Mutation Planet" (1973) by Barrington J. Bayley as per Planet of animals that evolve in minutes?
Filled with ominous mutterings, troubled by ground-trembling rumblings, the vast and brooding landscape stretched all around in endless darkness and gloom. Across this landscape the mountainous form of Dominus moved at speed, a massed, heavy shadow darker than the gloom itself, sullenly majestic, possessing total power.
It can apparently be read online here.
I believe you would be talking about the text by Ray Bradbury, "The One Who Waits." It begins in a well on Mars and the bacteria/alien takes over each human causing them to kill themselves then taking host of someone else.
I live in a well. I live like smoke in the well. Like vapor in a stone throat. I don't move. I don't do anything but wait. Overhead I see the cold stars of night and morning, and I see the sun. And sometimes I sing old songs of this world when it was young. How can I tell you what I am when I don't know? I cannot. I am simply waiting. I am mist and moonlight and memory. I am sad and I am old. Sometimes I fall like rain into the well. Spider webs are startled into forming where my rain falls fast, on the water surface. I wait in cool silence and there will be a day when I no longer wait.
Could it be Dragon's egg?
Dragon's Egg is a 1980 hard science fiction novel by Robert L. Forward. In the story, Dragon's Egg is a neutron star with a surface gravity 67 billion times that of Earth, and inhabited by cheela, intelligent creatures the size of a sesame seed who live, think and develop a million times faster than humans. Most of the novel, from May to June 2050, chronicles the cheela civilization beginning with its discovery of agriculture to advanced technology and its first face-to-face contact with humans, who are observing the hyper-rapid evolution of the cheela civilization from orbit around Dragon's Egg.
