First, we suppose greedily that our dream team wins all of its missing matches. After this, it should have P points. Then, build a graph with nodes x₁, x₂, ..., x_n - 1. Now, between x_i and x_j (i ≠ j), put an edge in each direction with capacity equal to the number of games missing between teams i and j. Use a node B, which has an edge towards every x_i with capacity equal to the number of matches the i^th team still has to play, and a node E, in such a way that there is an edge from each x_i to this node with capacity equal to P - p_i, where p_i are the points that the i^th team already has. Your dream team can be a champion iff the maxflow from B to E equals the number of missing matches.

This is a famous Max Flow problem, more info here