Is the offer and acceptance that took place in the presence of witnesses considered a marriage, knowing that it was agreed that the official marriage contract would be after two months?

If by "offer and acceptance" you mean that they took place in the presence of two witnesses, and the guardian or his representative consented to marrying you off, and you or your representative consented to the marriage, then the marriage contract is valid even if it was not officially documented. However, if you mean the suitor's request for the girl from her guardian and their consent, then this is an engagement and not a legal contract, because it is merely a preliminary step to the legal contract, and the rulings of marriage do not apply to it.