I am not familiar with the details of metallurgy and what things can be done and the technological requirements for those things. However, I can tell you that we have excavated large copper ingots from shipwrecks in the Mediterranean, including the Uluburun shipwreck from the late 14th century BC (~1325 BC, give or take a couple decades) and the Cape Gelidonya shipwreck, which is dated to about a century later (so around 1225 BC, give or take a couple decades). For further reading on Uluburun, see Pulak, Cemal. “The Uluburun Shipwreck: An Overview”. The International Journal of Nautical Archaeology, 27.3 (1998): 188–224. For further reading on Cape Gelidonya, see Bass, George F. "Cargo from the Age of Bronze: Cape Gelidonya, Turkey," in "Beneath the Seven Seas," edited by George F. Bass, pp. 48-55. New York and London, 2005.

These ingots were in a form called "oxhide ingots" which looked like this with a human hand for scale. These weighed between 20.1 and 29.5 kg after being cleaned of corrosion.

Macroscopic observations of the Uluburun ingots show that they were formed from multiple pours into the mold, according to John Merkel, "Ancient Smelting and Casting of Copper for 'Oxhide' Ingots," Studies in Sardinian Archaeology, Volume II, ed. Miriam S. Balmuth, (Ann Arbor: The University of Michigan Press, 1986), 260.

Note that these were not finished goods, but rather accumulations of copper and tin into easily measurable and transportable amounts, and were actually rather brittle (perhaps intentionally so) but highly pure (less than one weight percent of trace elements and about 99 percent pure copper).

In terms of finished goods, I have not seen any artifacts that are really thick chunks of metal. I haven't seen any like, chariot axles for example, made of bronze. This is one of the bigger metal artifacts I have seen from that period, and this other one from 1000 BC has a diameter of 11 cm according to the University of Pennsylvania Museum.

So to answer your question, did they make metal objects thicker than a quarter inch? Yes. Did they make finished bronze goods thicker than a quarter inch? I'm not sure, but I haven't seen any. If they have, they might have been something like an axe head or a sword like this khopesh from the 1200s BC Egypt. Most bronze objects are quite thin, possibly to reduce the expense (tin especially was very hard to come by, having to import it from Turkey or Afghanistan). I have not seen anything thicker than the things I have linked, but since as I said I am not a metallurgical expert, I don't want to say they never did.