Omega Speedmaster - Milo Ventimiglia - The Art of Racing in the Rain
About the watch
The watch seems to be an Omega Speedmaster 'Reduced'. The 'Reduced' Speedmaster is so called because of its smaller size (39mm case) than the regular Omega Speedmaster 'Moonwatch'. (which measures 42mm). The 'Reduced' also has a completely different movement, an automatic movement compared to the manual wound Moonwatch models.
The dial of the watch is more compact, with the subdials closers to the outer hour markings. Also notable are the minute markings (05, 10, 15 etc) inside the hour markers.
The product number for the Omega Speedmaster Reduced was ST.375.0032 (steel bracelet) or 3510.50.00 in Omega's newer (since the 1990s) numbering system.
The Omega Speedmaster Reduced watch was produced from 1988 until about 2006, and now available only in used watch stores or on eBay for $1000-$1500, a bit less than a regular Speedmaster 'Moonwatch'.
About the straps and bracelet
In early scenes of the film, when the main character Denny Swift (a race car driver played by Milo Ventimiglia) gets his dog 'Enzo', he wears the Speedmaster watch on a 'James Bond' Nato strap: the strap that has become famous as the James Bond Nato strap because Sean Connery wore his Rolex Submariner on a similar strap in the 1964 movie Goldfinger. The strap worn by Connery was actually slightly different from a Nato strap, but the colors of the current 'James Bond' Nato straps are similar: dark blue and green with red lines.
The Nato strap in the film has the dark blue/green/red colors and black PVD hardware (buckle and rings), very similar to (or it even might be) the Watch Gecko Vintage James Bond strap (available here).
Later in the film, the character is wearing presumably the same watch, but then on the original steel Omega Speedmaster bracelet that came with watch.
About the film
The Art of Racing in the Rain is a 2019 comedy-drama film directed by Simon Curtis (Woman in Gold, Goodbye Christopher Robin) based on the 2008 novel of the same name by author Garth Stein. The film stars Milo Ventimiglia, Amanda Seyfried and Kevin Costner as the voice of Enzo the dog.