By ‘first Sundays’ I understand you to mean first Sunday of the month.  There is no scriptural support for this to be done as infrequently as monthly.  In the first century, it seems that the church gathered on the first day of the week to remember Jesus in breaking bread.

Acts 20:7:

On the first day of the week, when we were gathered together to break bread, Paul talked with them, intending to depart on the next day, and he prolonged his speech until midnight.

Although the following passage doesn’t say they broke bread, it seems highly likely they did – 1 Corinthians 16:2:

On the first day of every week, each of you is to put something aside and store it up, as he may prosper, so that there will be no collecting when I come.

The following passage seems to indicate that they broke bread more often than weekly – Acts 2:42 & 46:

And they devoted themselves to the apostles’ teaching and the fellowship, to the breaking of bread and the prayers.  …  And day by day, attending the temple together and breaking bread in their homes, they received their food with glad and generous hearts

Although there are no Scriptural commandments about the frequency of communion,  it is important that we remember how Jesus died for us by sharing the bread and wine, as often as we can.  1 Corinthians 11:26:

For as often as you eat this bread and drink the cup, you proclaim the Lord’s death until he comes.

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