When the affidavit draft becomes a "true" affidavit, that is, when the oath is taken or affirmation made before an authorized official. In most cases, this correspond to the time of signature, although technically it is the moment when you state your affidavit to be true under oath to the notary or other authorized persons.
For unsworn declarations made under penalty of perjury, in jurisdictions that allow them to be used in lieu of affidavit, it becomes valid at the time of signature and a perjury would be committed then.