I think you will find that S355J2G3 is an old designation (EN10025:1990) which was replaced in 2004 with S355J0. If you want an equivalent then it has a yield of 355MPa and guaranteed impact properties (Charpy test) of 27 Joules at zero degrees Celsius.
An ASTM equivalent would be A572 Grade 50 which has a yield of 345 MPa but you would need to invoke supplementary clause S5, and state requirements, to get the impact properties.
The J2 means 27J @ -20°C, J0 means 27J @ 0°C. Couldn't immediately find the meaning of G3, have to search in my old standards.
Yield = 355MPa, the S stands for Structural steel.
Correct that the J2 has been replaced with J0, however I'd still search for something with 27J @ -20°C, just to be sure... Can't be too hard.
S355J2G3 was defined in EN 10025:1990.
J2 : a minimum Impact Energy of 27 J at -20°C (Charpy-V-specimen in longitudinal direction, average of 3 values)
G3 : the delivery condition is normalized for flat products (plates, coils, sheets). For Long products (sections, bars,..) the delivery condition is at the discretion of the manufacturer unless otherwise agreed.
In EN 10025-2:2004 S355J2G3 was replaced either by S355J2+N for flat products or by S355J2 for long products.