They were not immediately aware of the nature of the attack, other than it was a major attack. 16 hours after the bombing, the United States released a statement by the President (and then considerably follow-up information) claiming it was an atomic bomb. The Japanese high command responded by sending a team of scientists, lead by those who had been working on their own very small nuclear fission program (just a research program, not a production program), to Hiroshima to inspect the city and report back on whether it was in fact an atomic bomb. Yoshio Nishina, who had headed one part of the Japanese research, traveled from Tokyo to Hiroshima and examined the evidence from the blast and radiological residues. He cabled back to Tokyo on the evening of August 8th, 1945:

What I've seen so far is unspeakable. Tens of thousands dead. Bodies piled up everywhere. Sick, wounded, naked people wandering around in a daze ... Almost no buildings left standing. ... I'm very sorry to tell you this ... the so-called new-type bomb is actually an atomic bomb.

There are more details on the timing here.