Aw ang cute ng tanong mo! Yes, normal lang yan, ang pusod ng baby ay usually may slight bulge pa for the first few weeks, at parang may itim na dried part pa from the umbilical cord stump na nakakapraning tingnan, pero lalabas yan on its own within 1-2 weeks pa lang. Kung makikita mo namang may unusual discharge, foul smell, o redness around it, mas better mag-check ka na with your pediatrician para safe, kaya lang, pero in general, what you're seeing ay totally normal sa 1-month-old babies, kami rin ng mga kaibigan ko napanic dito haha!