Making window opening larger is not all that hard. However it will require you to remove the sheetrock and the siding. Yeah I know it kinda stinks.
You can use either 2 2×10’s or 2 2×12’s. This is going to really depend on your prints and specs needed. All new house’s I build are built with double 2×10’s with jack studs one on each end of the header and a king stud along the side of the header. All nailed with common 12 nails. 3″ screws if you like.
Never just measure the window and make your opening that size. Always go at least 1″ larger both sides. By making the opening bigger will allow you to adjust for level.
How to determine if your window meets egress
With the window open you’ll need a minimum 24″ x 34″ of 5.7 sq feet
To Determine your window you would simply measure your opening and divide it by 144. Example if your window measures 33″x 23″ = 759 ÷ by 144 and will give you 5.27083333 So 5.27 and it’s too small.