So I mean of the many many hundreds of bombs that were exploded for testing purposes, are there any humans that died by being caught up in the explosion? I'm not interested in deaths months or years later due to radiation, only in immediate deaths from the explosions. Perhaps someone was too close or an island villager who wasn't evacuated or an airplane that got caught up in the explosion, something like that.
Yes. Excluding radiation-related injuries, three people have died in the course of nuclear testing for effects related to blast. The first two were during the first Soviet H-bomb test in 1955:
On 22 November 1955 the USSR conducted its first test of a multi-stage thermonuclear device. The device, the RDS-37, was designed as a nuclear gravity bomb with a full yield of about 3 megatons. The test version was modified to reduce the yield to an expected 1.45 megatons, to reduce the risk to the local population. It was airdropped from a Tupolev-95 bomber over Technical Area Sh ("Ground Zero") at the Semipalatinsk Test Site in Kazakhstan. It detonated with a yield of 1.6 megatons at altitude of 1,550 meters. Civilians in nearby villages had been warned as a precaution, but one child who ran back into a house immediately after the detonation was killed when the blast wave arrived and caused the roof to collapse. Another 42 were injured by glass fragments. A trench collapsed onto soldiers observing the detonation at 36 km from ground zero, killing one from suffocation and causing contusions to five others.
The other was an American who died during an American underground test in 1984:
At 17:00 UT (10:00 AM local time) an underground test was conducted at Rainer Mesa in the Nevada Test Site. The test, Midas Myth or Milagro, was designed to investigate weapon effects and involved a device with yield between 0 and 20 kt (likely closer to 20 kt) in a tunnel at a depth of 361 meters. Shortly after the test technicians went to equipment trailers at ground zero. While there, the column of rock above the test collapsed 3 hours, 13 minutes after detonation, causing the surface at ground zero to collapse into a crater 113 meters across and 5 meters deep. Such collapse pit formation, while typical for underground tests, was not expected so soon after detonation in this case. The collapse caused injuries to 15 personnel, one of whom later died of his injuries. In addition, the emplacement tunnel collapsed to a greater extent than expected, causing damage to experimental equipment. No radiation release occurred, and there was no personnel radiation exposure.
These are the only documented test-related injuries that were nearly immediate and not related to radiation exposure. If you include radiation exposure you range from at least 1 (the Lucky Dragon incident, 1954) to thousands (fatal cancers from fallout of atmospheric testing, not easily directly attributable).