Hey Pix,
So much good advice so far. I agree with Robin that it's easier to hit on some ukes than others due to neck widths, string spacing, and string distance from the edge. This is the excuse I give myself to own multiple ukes.
How I tackled this G chord with G string note is deconstructing it and going backwards. Each hand and instrument is different and i can't stretch or bend my fingers like Aldrine Guerrero does in his tutorials so I had to adapt to what I could do.
Put your ring finger on the 4th string, 4th fret
Put your middle finger on the 2nd string, 3rd fret
Pluck each string and make sure each note rings
Keep looking at your ring finger to see how much wiggle room you have before you mute the 3rd string, and remember it.
Barre your index finger on the 2nd fret. Depending on your fingers and reach, you may need to barre all 4 strings or just 3 strings. Just look at your fingers from different angles to find a grip that works with your hand. You may need to move your palm closer or further away from the fretboard.
For me, I need to barre the entire 2nd fret to hit the 4th string with my ring finger. It's going to differ for each person. Now once you have a mental picture of how you need to hold it. Don't worry about the strength as that will come over time. Now practice this chord everyday by squeezing and letting go while you pluck each string clearly. Don't do it for too long or your hand will tire out.
It took me a couple weeks for my hand to get used to it. I practice by putting the fingers in the right position and usually starting backwards with the ring finger. Once in position, then press down hard for a second, ring out each note clearly, then rest. It's all muscle memory and how you need to adapt for your hand.