As a young child, the Kotzker Rebbe is quoted as asking how Klal Yisroel in the Wilderness were able to fulfill the mitzva of tzedaka if they had everything they needed with the manna. However, they don't report an answer - how did the Jews fulfill this mitzva after matan Torah in the Wilderness? (If there was no obligation to give tzedaka, then what was the Kotzer Rebbe's question?)
I can think of two ways that one could have fulfilled the mitzvah of tzedaka back then.
If one knew someone who needed to travel away from where klal yisroel was encamped and since the manna would have spoiled the next day (and they wouldn't get manna where one was travelling on the way) so giving them some money would be considered tzedaka see shulchan aruch: someone who normally has means but is traveling and is in need during the trip
One could have donated to the mishkan or another public need and that would be tzedaka. See chachmas adam 148
Lastly, just as a thought, instead of doing tzedaka, one could have replaced that mitzvah with doing chesed which the gemarah calls it greater than doing tzedaka and one can do it to rich people (fellow klal yisroel who had manna to eat) as well. See gemarah succah 49b
I saw somewhere that the Gerrer Rebbe also asks this question. He answer that there is a Midrash that the Manna tasted like whatever one imagined. Many Israelites in Egypt had experienced a limited repertoire of foods. So those who had eaten an unusual food could share their recollections. In a way they gave charity. Which shows us that charity is not only material it is also charity, Tzedakah, when we share our imagination with someone.