When you start running a pruned node, your node still has to verify each and every block, from the genesis.
As far as I know, this is incorrect.
They do not have the entire blockchain so they cannot verify from the Genesis block. A pruned node can only verify after a determined block, which is stored in the node.
So you have to trust that you received the transaction history from a "trusted user". And that that history is correct.
A full node just need to know that the Genesis block is correct. That's easy to check. But check the entire pruned blockchain is not.
Spv nodes are completely different and do not verify transactions, just look for transactions related to the wallet addresses from other full nodes.
Please correct me if I said something wrong.
@Heisenberg_Hunter, I was lucky and I was able to find this amazing answer from @achow101:
What you are describing is an idea that has been floating around for several years now. You're not the only one to think of it.
The reason it has not been implemented is because it introduces some centralizing trust. Right now, a new node coming only has to verify every single block and confirmed transaction since the beginning of Bitcoin. In doing so, they are able to build the UTXO set themselves and check that everything is correct. The only trust is that the genesis block is correct, and if it is not, it's extremely obvious that it is wrong. However changing it so that the "genesis" is really the UTXO set at a certain height means that there is going to be more trust. Now you have to trust that the UTXO set is correct. But without having the full blockchain history, how can you prove that that UTXO set really was the UTXO set at the cutoff point?
Additionally, the UTXO set is kinda big. It isn't really something that you want to package with a software. But you need to get it somehow. Well now you need to trust that whoever gave you the software (either packaged or over the network from another node) haven't changed the UTXO set. Changing the UTXO set would not be as obvious as changing the genesis block. You could simply add an extra UTXO and basically no one would notice. It wouldn't be noticed until the UTXO was spent, and if done at the right time (when no nodes with the full history remain), would be completely unnoticed.
To combat that, you could say that miners have to include the hash of the UTXO set in their blocks, or maybe even just the hash of the UTXO set for the block immediately after the cutoff. But now we have someone else we need to trust: miners. Now you need to trust that miners have used the correct hash. You need to trust that whoever is producing the UTXO set hasn't colluded with miners to insert a fake UTXO into the UTXO set. If they did, you would have the same problems as earlier, and it would seem like the UTXO set checks out since the hash is also in a block.
There are other possibilities too that have been discussed elsewhere. But the issue with this idea in general is that it involves more trust. And in a system where the goal is to have as little trust as possible, that is just not going to happen.