What would you need to explore space? There are some ideas in science fiction like interstellar arks and near lightspeed travel. But one concept might be easier to realize: Self-replicating, autonomous machines.
The Problem of Interstellar Arks
Interstellar arks are space ships that are of enourmous size. They are big enough to have enough humans on it so that those humans can have childens over an limitles time without getting into trouble because of incest. Traill et al.  suggests that you need about 4000 individuals for a minimal viable population.
Those 4000 people would need food, air, personal space. You would need resources to repair the ship and explore planets. Medicine. You would need fuel. That would be a lot of stuff.
Bringing stuff from earth to space is expensive.
And those people would eventually be trapped on that ship for many, many generations before they might find another habitable planet. You might eventually need to do terraforming. I can't even imagine the number of resources that would be needed for that.
The next problem is that you would want the explorers to keep contact with earth. Those signals would either have to be highligh redundant (see error correcting codes) or they might get received only partially. So eventually you would like to get relay stations that catch up the signal, correct errors (or request a new send of the broken part) and send it again.
An ark would have to carry everything for that. That's a problem because sending so much stuff from earth to space is expensive.
The alternative: Replicating Machines
An alternative might be replicating machines. Machines don't need personal space. They don't need air. They don't need food or medicine. They don't run into psychical problems.
But they do need energy. They need resources. And they either need to be really intelligent or they need to have clear instructions.
I a working minimal space exploring construction kit (let's call it MISECK, because that's much shorter than 'minimal space exploring construction set') should be able to do the following:
- Construct other MISECKs from resources that can be found in space (e.g. on asteroids, moons or planets). The plural was intended. Every MISECK would have to be able to produce at least two other MISECKs.
- Build communication satelites: That communication satelite would act as a relay station. It talks with other satelites, receives messages and sends messages. It is able to check if the received message has errors and request a new message in case of errors. They should also store as much information as possible. This way, one could eventually contact them and get information that might otherwise get lost.
- Build exploration satelites which can gather information about a planet. This information should be send to the communication satelites and finally back to earth.
- Build mining and construction robots that are able to mine all resources needed to construct MISECKS. That will include melting ore and constructing fabrics which are able to produce computer chips.
- Build power plants. Those might be solar cells, fusion/fission reactors or something completely different. But something has to provide the energy to make it possible to run all those machines and to travel enormous distances in space.
- Explore and coordinate: This is a collaborative planning task. MISECKs have to know where other MISECKs are. If one MISECK gets destroyed by anything, there might still be something that is worth exploring.
- Interstellar travel
- Intergalactic travel
- Smallest viable reproducing population