Question: Can I light a memorial candle for someone deceased less than 30 days?
Answer: You "can" light a candle, just as during shiva a candle was lit. The Rabbis taught that "the soul of a human being is a light honoring God."
However, it is more traditional to wait to light a yahrzeit light (memorial candle) until three Festivals have passed. Perhaps the rationale is to prevent unnecessary mourning, encourage the mourner to "move on" in their lives and resume some semblance of normalcy as a way of coping with loss. If people continue to mourn, e.g. visit the cemetery too frequently. There are people I've known who just "had" to visit weekly for years - this becomes an unhealthy psychological coping, and I have in my experience encouraged them to seek professional assistance. Death is part of life, and while the death of loved ones is traumatic and of the greatest pain, we can live in the "now" or certainly not in the "past" but need to look forward - and as the Torah teaches "choose life."
So, you may do so, but I would encourage you to speak with your rabbi about what is most appropriate for you and your family.