Can you give matanos l’evyonim before Purim? Shalach Manos? on the Night of Purim?
Mishloach Manos is a Purim-day mitzvah. There's talk about asking a proxy in advance to deliver them on Purim day for you, which should probably be okay.
Matanos L'Evyonim should either:
You're not supposed to give matanaos l'evyonim too long before Purim, as the poor person may have already consumed the gift by the time Purim comes around. (And if someone is struggling, to hand them a large check and say "you can't use this until next week!" shows you're missing the point.)
Similarly, "if you look around on Purim day and there are no poor people in the town", you can either set aside the money on Purim day, to use later; or mail the money on Purim day.
So if your synagogue has a collection a few days before Purim (or Purim night) that will be distributed on Purim day, that's fine.
A number of rabbonim will collect earlier because they know of poor families that require the help. You can give to organizations that give out meals on Purim so that families can have a seudas Purim and do not have to buy for themselves. I would think that it might be better to give through an organization or Rav because the money will be collected and used to buy sufficiently for the aniyim to get sufficient for their needs as what one individual can afford to give may not be enough.
Many organizations nowadays sell cards showing that you are giving matonos l'evyonim rather than mishloach manos. As long as you give the required mishloach manos, this is actually considered better for you to do.