A process for manufacturing a composite part includes arranging a fibrous preform in a mold including an impregnation chamber which includes in its lower part a filter by making a first face of the preform rest on the filter, the impregnation chamber being closed by a flexible membrane placed opposite a second face of the preform, the membrane separating the impregnation chamber from a compaction chamber. The process further includes injecting a compression fluid into the compaction chamber so as to apply a first pressure on the membrane and injecting a slurry including ceramic particles into the impregnation chamber with a second pressure while maintaining the injection of the compression fluid, the second injection pressure of the slurry being lower than the first pressure on the membrane.