Is this possible with Ethereum?
Here are some of the different options on syncing with
"Full" Sync: Gets the block headers, the block bodies, and validates every element from genesis block.
Fast Sync: Gets the block headers, the block bodies, it processes no transactions until current block - 64(*). Then it gets a snapshot state and goes like a full synchronization.
Light Sync: Gets only the current state. To verify elements, it needs to ask to full (archive) nodes for the corresponding tree leaves.
Light sync is execute with
geth --light and it is likely what you are looking for.