Short answer
Four checks settle most cases: case diameter, bezel engraving, date position, and caliber number. A real Speedmaster "1957" reissue measures 40.5 mm (2022) or 41.5 mm (2013) across the case, has a tachymeter scale cut into the bezel and filled, puts the date at 6 o'clock, and shows a caliber number under the sapphire back that matches the reference on the card. A replica fails at least one of those four.
What "4th gen" refers to
Omega does not use that term. The 1957 original is reference CK2915, built in three variants: CK2915-1, CK2915-2 and CK2915-3. The modern reissue is the Speedmaster '57, released in 2013 and revised in 2022. A seller who says "4th gen" means one of those watches, or a replica of one. Ask for the reference number first. If the seller cannot give it, stop.
Case size
Measure the case from 3 to 9 o'clock, crown excluded, with a caliper. 2013 Speedmaster '57: 41.5 mm. 2022: 40.5 mm. Original CK2915: about 38 mm. Replica cases run wide of spec by 0.5 mm to 2 mm, and a thicker bezel often hides the extra width.
Bezel
Tachymeter numerals on a real '57 are engraved into the metal and filled with paint. Drag a fingernail across the scale. Real: a step down into each numeral. Replica: a flat surface with print on top, or a shallow laser mark with no fill depth.
Dial and date
Date window at 6 o'clock on every Speedmaster '57. Subdials at 3 (60 minutes), 6 (12 hours) and 9 (running seconds). Under a 10x loupe, real printing holds a hard edge. Replica print shows ink spread and uneven spacing in the word "Speedmaster".
Hands
Broad arrow hour and minute hands. The luminous fill sits level with the metal frame on a real watch. Replica fill sits proud of the frame, shows bubbles, or turns yellow in months.
Caliber
2013 '57: caliber 9300 or 9301, automatic, 28,800 vph. 2022 '57: caliber 9906, hand wound, 28,800 vph. The 9906 has no rotor. A rotor under the back of a watch sold as a 2022 '57 is proof of a fake. Read the number engraved on the bridge and compare it with the reference.
Papers and serial
Master Chronometer card from METAS, with the serial. METAS tests the movement to 0/+5 seconds per day and 15,000 gauss. The serial on the card, the movement and the case must match. A card with a mismatched serial, or no card, is a problem on any watch at this price.
What photos cannot show
Bezel engraving depth, lume fill level and the movement under the back. Ask for an angled macro photo of the bezel and one of the caliber engraving. Run a timegrapher check when the watch arrives, and buy with a return window. Caliber beat rate and amplitude data are published by Omega per caliber, so compare the readings with the spec sheet rather than with a memory of one.