Our food stamps were approved and received the same day. Well, the first time we were on it, it took about a week but that was b/c we were missing one piece of paperwork and it took that long for my DH to get it to the office. We went off them for a while and when we went back in them, the money was loaded onto our card the same day. However, it can really depend on how busy your office is where you live. Where I live, people have to line up early and they are seen same day if they are in before 10 am. We also may have qualified for "emergency" food stamps b/c DH lost his job and we had no income coming in.
WIC usually takes longer b/c it takes longer to get an appt. Once you gt an appt, you should receive the checks the same day and can use them immediately. I despise going to the local WIC office but I suck I up b/c we need the help with food. Once one of gets a job, I am dropping it even if we still qualify. It's just not worth it for us but different offices are better than others.