I think it’s all in your attitude. If you’re confident with an “I got this” attitude I think it’ll make all the difference. If you’re unsure of yourself NP will probably be as well. Them feeling the need to step in to help or you apologizing may cause them to question your capabilities more than the baby crying if the crying is within reason and just crankiness and/or the normal causes, because it may come off as you being overwhelemed and not very confident in yourself.

You want the NP to have just as much confidence of the idea of them not being there as they would if they were. Not to mention them stepping in could be interfering with the bond you and NB could be forming making things harder when they get older because they may make it a point to cry more just to go to their siblings or parent instead, and they’ll know it works.