There are a variety of factors that contribute to the investment timeline. For example, if you are the lead investor who is setting the terms, you will do significantly more due-diligence and try to help the company circle some more new investors. On the other hand, if you are participating in a party round with no lead which is pretty common at the pre-seed stage, you may try to accomodate the rough timeline set by the founders and other investors.
A typical process takes ~1 month. However during cyclical economic slowdowns or the holidays, it's not uncommon for this timeline to be extended to to 2 months or more.