io.ReadSeeker is the interface that groups the basic Read() and Seek() methods. The definition of the Seek() method:
Seek(offset int64, whence int) (int64, error)
An implementation of the Seek() method requires to be able to seek anywhere in the source, which requires all the source to be available or reproducible. A file is a perfect example, the file is saved permanently to your disk and any part of it can be read at any time.
response.Body is implemented to read from the underlying TCP connection. Reading from the underlying TCP connection gives you the data that the client at the other side sends you. The data is not cached, and the client won’t send you the data again upon request. That’s why response.Body does not implement io.Seeker (and thus io.ReadSeeker either).
So in order to obtain an io.ReadSeeker from an io.Reader or io.ReadCloser, you need something that caches all the data, so that upon request it can seek to anywhere in that.
This caching mechanism may be writing it to a file as you mentioned, or you can read everything into memory, into a []byte using ioutil.ReadAll(), and then you can use bytes.NewReader() to obtain an io.ReadSeeker from a []byte. Of course this has its limitations: all the content must fit into memory, and also you might not want to reserve that amount of memory for this file copy operation.
All in all, an implementation of io.Seeker or io.ReadSeeker requires all the source data to be available, so your best bet is writing it to a file, or for small files reading all into a []byte and streaming the content of that byte slice.