Catalyzes the first and rate-limiting step of polyamine biosynthesis that converts ornithine into putrescine, which is the precursor for the polyamines, spermidine and spermine. Polyamines are essential for cell proliferation and are implicated in cellular processes, ranging from DNA replication to apoptosis. . This is the function of ODC1 (ornithine decarboxylase 1, Ensembl gene identifier ENSG00000115758).