The words "can only" mean that there is no other assumption to be made, and may also suggest the speaker's reluctance to come to such a conclusion. "I can assume" has a nuance that the assumption is deemed permissible, but actually "I can assume" does not seem very common to me. Much more common would be "We can assume".
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.