deferral of a Ph.D. position in Europe
Whether it is possible or not can depend on all sorts of things. The only people that can answer that truly are the people that offered you the position. You should ask them.

This is not an unreasonable thing to ask, and I can't imagine starting a month or so later would be much of a problem for a PhD (but again the only people that can tell you that are...). Negotiation of the starting date is a normal part of the hiring process.