The patient's painful big toe is most likely caused by:

The painful big toe is most likely caused by gout, a form of inflammatory arthritis characterized by sudden and severe episodes of pain, redness, and swelling in a joint. Gout commonly affects the big toe due to the accumulation of urate crystals in the joint, which can occur when there are elevated levels of uric acid in the blood. This condition is closely linked to dietary factors, alcohol intake, and certain medical conditions that increase uric acid production or reduce its excretion.

The acute attack often presents as intense pain and tenderness, making movement difficult. The association of gout with the big toe specifically is so prevalent that it is sometimes referred to as "podagra." This positioning of symptoms and the classic presentation makes gout the most likely cause in this scenario.