It's really OK to miss the first half of Mass... on weekdays!
That's my understanding, anyway; while - of course - one prefers to arrive on time and even earlier (so as to prepare and pray), if one doesn't get to church on time, as weekday Masses are entirely voluntary anyway, then one shouldn't think that one cannot turn up late, nor should one think that, if one is late, one shouldn't receive Holy Communion (as long as one doesn't arrive so late that it would appear scandalous).
After all, Canon Law provides that, even outside of Mass, a priest ought give Communion to those of the faithful who ask for It:
Canon 918 — It is most strongly recommended that the faithful receive holy communion in the course of a eucharistic celebration. If, however, for good reason they ask for it apart from the Mass, it is to be administered to them, observing the liturgical rites.
Through laziness, these days even priests too often palm off onto lay volunteers the task of bringing Holy Communion to the sick, and to them alone, perhaps only once a week or less; yet here it seems to suggest that a worker, for instance, who cannot get to a weekday Mass, but would have wished to, may ask his priest to communicate him.
An interesting canon! I suspect that it applied more in days of yore, when Mass could only be celebrated in the morning (from an hour before sunrise to an hour after noon).
Recall that in the old Basilica of Our Lady of Guadalupe in Mexico, such was the continuous press of humble pilgrims that the clergy were wont to distribute Holy Communion at the altar of the Blessed Sacrament every quarter hour.
I say it's alright to miss the first half, for the obvious reason that - as I perforce did to-day - if you miss the first half, you can later "catch up" by reading over the relevant parts from your missal (presumably skipping the Dominus vobiscum's).
It is just as obvious that missing the second half of Mass, the sacred Action, means missing out on the Sacrifice and Communion, which one cannot supply at home!
Remember, dear reader, Chesterton's saying: If something is worth doing, it's worth doing badly.
This certainly applies to the Novus Ordo, as exemplified in the liturgical practice of the Church at large; and it applies to the individual Western Christian in due proportion also. (I trust my sense of humour is evident here.)
While of course one cannot "make Eucharist" at home (apologies for the rather modern jargon), one can at least read the first half of Mass, as a sort of paraliturgy (that dreadful term so often used in my youth for funny made-up Catholic "rituals", loosely based on the first half of Mass).
Anglicans of course will denominate the first half of the Mass the Ante-Communion, a good term, since it points out how the preparatory rites and Scriptural lessons are all ordained and oriented toward the second half of the service, what Catholics call the Liturgy of the Eucharist, and what Anglicans call the Holy Communion or the Communion Office.
Just as Exposition and Benediction is meant to be not merely a service of worship of Our Lord in His Sacrament, but an expression of our yearning to receive Him worthily, since the Eucharist was instituted ut sumatur (that It be consumed); so the fore-Mass (as Pius Parsch called it) is fundamentally ordered toward the second half of the Mass, the more important part, the sacramental service.
Everyone knows, after all, that the two parts of Mass derive from two different sources: the Synagogue service of prayers and readings; and the Last Supper. Very early in Apostolic times the two were brought together and united; but there are isolated examples until quite late of the Supper of the Lord being celebrated separately - apparently my favourite example of liturgically-minded Separated Brethren, the Scottish Episcopalians, sometimes did this in the eighteenth century...