No, I don't think so. My understanding is that the Beirut harbour bombing was not a bombing, per se. It was the explosion of a large store of fertiliser (something like 3000 tonnes of it!) held in that area. The fertiliser was from a transport ship that went bankrupt at the harbour some six years previously and its cargo (the fertiliser) confiscated and stored in a warehouse there alongside, of all things, a store of fireworks. At some point the fireworks exploded, caused a fire, and a few seconds later the fertiliser exploded.
So no. I can't consider that explosion proof of a nuke. In order to prove to me that there are no nukes you will need to prove to me that England, France, China, Russia and the USA - and now North Korea - were all in on it as they had their nuclear programmes as well - was it a conspiracy among nations? I don't think so. Take the Tsar Bomba nuke tested by the USSR in 1961 - a 50 Mt monster. The test was even monitored by the USA at the time. You would need to prove to me that it never happened and that both the USSR and the USA were outright lying about it. That would require a lot of proof.
As for Miles Mathis, I got a peek at his write-up on Trinity using the link graciously provided by Billy Masterson above. I haven't got through all the article yet, but the first few paragraphs already alerted me to something wrong with his conclusion that the Trinity test was a fake. He showed a photo of a group of Army guys surrounding a script for a film about the Trinity test. He claimed that you don't write scripts for real events you are filming - you only write scripts for movies. Well, right away he is entirely wrong. All documentaries have written scripts for the narrator of the documentary. The Army chaps shown had the responsibility of producing that documentary as it was an army project, I would imagine. I will try to continue through his paper, but my antennae are already sitting straight up.