This paper investigates whether the Critical Period (CP) effects in human language acquisition are observed in self-supervised speech models (S3Ms). CP effects refer to greater difficulty in acquiring a second language (L2) with delayed L2 exposure onset, and greater retention of their first language (L1) with delayed L1 exposure offset. While previous work has studied these effects using textual language models, their presence in speech models remains underexplored despite the central role of spoken language in human language acquisition. We train S3Ms with varying L2 training onsets and L1 training offsets on child-directed speech and evaluate their phone discrimination performance. We find that S3Ms do not exhibit clear evidence of either CP effects in terms of phonological acquisition. Notably, models with delayed L2 exposure onset tend to perform better on L2 and delayed L1 exposure offset leads to L1 forgetting.