Ten Gathered for Mincha After Ten

What is the ruling if Mincha was started without ten people in the synagogue, and after finishing Ashrei, ten people arrived? Can the Kaddish before the Amidah be recited?

They should recite three verses, and then say Kaddish.

The Taz in Orach Chaim, Siman 55, Se'if Katan 3 writes: "But certainly, if it happened that the minyan did not gather until after Ashrei, this should not prevent the Kaddish from being said. This is the daily practice when reciting Psalms in the morning without a minyan, and then when the minyan gathers, they say Kaddish, and this is proper." However, the Magen Avraham in Siman 234, Se'if Katan 1 writes: "If Ashrei was said without a minyan, and then a minyan gathered, they should say one Psalm and then Kaddish. And it seems to me that the same applies when learning in the synagogue without a minyan, and then ten gather to say Kaddish, this is not proper. For the main reason for Kaddish is the sanctification of the Name, and therefore ten are needed at the time of learning, as we derive from 'and I shall be sanctified among the children of Israel', and see Siman 157." Practically, the Mishnah Berurah in Siman 55, Se'if Katan 2 rules to say three verses and then Kaddish.