Yes, mute the strings with your fingerboard hand and spend some time focusing on just your picking hand, eyeballing it as you do. Alternate picking on each string, then when you can do that accurately, try going between B&A, E&D, A&G (like you would play octaves), again alternate picking as you go (1+2+3+4+ on each string at first). When you can do that accurately and consistently with minimum hand movement, mix it up how you feel like.
This will help internalise the new string spacing which is what we all trip up on at first, picking especially.
Won't take too long. Have fun, it's a good game!