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This is a book I read in the 70's, but it could have been written at an earlier time.
In this story, there was a technology that could reach out into space and view the universe from remote locations. The views were so detailed that, for instance, the scope could reach out and look back on the Earth, and see what was there in the past.
There were multiple levels of this technology that could reach further and further out, and still view with amazing detail.
Is this Macroscope (1969) by Piers Anthony...?
A group of earthlings begins an exploration of the unknown when they enter the Macroscope, a doorway through time and space
From Wikipedia:
The central plot device is the "macroscope", a large crystal that can be used to focus a newly discovered type of particle, the "macron". Macrons are not subject to many of the effects that interfere with light, and as a result the macroscope can focus on any location in space-time with exceptional clarity, producing what is essentially a telescope of infinite resolution in the space-time continuum. The macroscope has been built into a solar-orbiting space station where scientists visit to book time on the device. Using it, they are able to explore space as never before.
Not a short story... But in L. Ron Hubbard's Battlefield Earth
The humans are using a teleporter they captured, to "Send" then "Retrieve" a camera with perfect optics.
They "send" it two lightyears from a planet. Have it record the planet for a few hours. They are looking for an event that took place about 2 years before (since the light from 2 years ago is just reaching that point in space.) Then "retrieve" it to see what it saw.
They then start adjusting the exact distance (2.05 lightyears, 2.07 light years, etc.) to find and see the event they are looking for that took place on the planet.
It's a short story, but is there any chance you're thinking of Isaac Asimov's "The Dead Past"? It involves a Chronoscope, which can see into the past, but is strictly controlled by the government. When a scientist builds his own chronoscope, he finds that it actually can't see more than 120 years into the past due to increasing noise. When the government catches up to him, they explain that, since the Chronoscope can see anywhere in the recent past, it's the ultimate spying mechanism, and that's why they've been suppressing further discovery.
If nothing else, it has a list of similar stories that might lead to the correct answer.
This is a bit of a stretch, but potentially this could be Arthur C. Clarke and Stephen Baxter's The Light of Other Days
The technology here is the WormCam, it is a remote viewing wormhole that allows one way information travel. The opening scenes show the tech being used to steal political secrets, about 1/3 of the way into the book a demonstration is used of a remote viewing of Saturn eighty light minutes away a huge step up with the technology that then allows for a similar wormhole 'setting' where the location is still on earth, but now looking into the past.
If I restrict the spacelike interval to a couple of metres the rest of the wormhole span becomes timelike...'
And the first demo shows the lab eighty minutes into the past.
The tech scales up several times during the story, in capability and in convenience.
This is absolutely not something you could have read in the 70s being published in the year 2000. But the direct juxtaposition of viewing remote objects in space and then the past made this seem a potential match.
I'm pretty sure this is not it, since it doesn't match much of your description, but could you be thinking of "I See You" by Damon Knight, perhaps mixed with one of the other answers here? "I See You" was published in the 70s, and involves a time viewer that can see the past, but it doesn't involve doing so from space.
The rest of your description really reminds me of The Light of Other Days (as per @Jonita's answer), but that's obviously too late for when you remember reading it. But if you were conflating two different (but similar) stories, that could explain it.
