To start...

How is the shifting up/down the cassette in the other gears, 3 thru 9?

Can you shift to the largest cog, notwithstanding the poor shift from 3 to 2?

If you can shift to the largest cog, how is shifting up to 2 and 3?

There really should be no need to adjust the high/low limit screws after the initial derailleur install, with the possible exception if you change cassettes or wheels.

Had your RD been bumped immediately prior to this problem, such as laying the bike down, crash, loading/unloading in vehicle, etc? If shifting is otherwise good in 3 thru 9, you may have a tweaked hanger. Whenever you're performing derailleur adjustments, you want to start with a straight hanger. You can do a visual check from the rear of the bike to see how well the two derailleur pulleys and the cog line up, however 9+ speeds are finicky enough that an alignment tool may be required.