The existing answer essentially says there is a debate (of course there is, it is a point of Halacha), but you can wish someone "Shabbat Shalom" on Friday before Mincha. What about Thursday, or even, possibly, Wednesday? I have heard it said that this is also acceptable (and I am thinking especially of people I might/will not see on Shabbat).
Shalom, Thank you for your question. As was explained in the previous question (https://www.yeshiva.co/ask/2968 ) there is an opinion that perhaps saying "Shabbat Shalom" might be considered as if is accepting the holiness of the Shabbat upon themselves, in which case it would then be problematic to recite a weekday Friday afternoon Mincha. (There are though many who believe that this is not a problem). As we wrote at the end of the answer, this issue only applies during the time-span that one could really accept the Shabbat, that is from "plag ha-mincha" (a halachic hour and a quarter before nightfall). Before this time, even if a person did declare that they accepted the Shabbat upon themselves, it would be to no avail – all the more so just saying "Shabbat Shalom" would not entail any problems of perhaps accepting Shabbat by mistake. With this in mind, to answer your question, it is allowed to wish people a Shabbat Shalom any time earlier in the week as one feels is appropriate. For example, if you see someone on Sunday and they tell you that they're going to a special Shabbat this week for their brother's Sheva Brachot (wedding party), and you will not be seeing or talking to them before Shabbat, you could wish them "Sounds great, have a Shabat Shalom". (I personally knew a very holy Rabbi who wished people "Shabat Shalom" all week long, in order to for fill the mitzvah of remembering the Shabbat day, every day of the week. This though was considered as unusual.) Blessings – and …. Shabbat Shalom!