You cannot use your dad's Costco membership card without him being present. The individual named on the card must be the one using it, as the card is non-transferable. This rule also applies to family members, so you cannot use your dad's Costco card if he is not with you. However, there are some exceptions to this rule.
For example, if your dad has passed away, you may be able to use his Costco membership card if you have proof of death and a letter from the executor of his estate authorizing you to do so. Additionally, suppose your dad cannot physically accompany you to Costco. In that case, he may be able to provide you with written authorization that would allow you to use his membership card without him present.