I concur with Snapdragon. Have you looked closely? It appears to me to be one bushy plant regrowing from the base of last year's plant rather than a clump of seedlings. They would hardly be on the point of flowering in zone 5 (which they are) if they had only germinated this spring. The plant's dead foliage and last years seed pods are clearly visible in the photo.

Compare with Portulaca oleracea, purslane. I won't pronounce on whether it is a 'weed' or a 'plant' - depends who you ask. Here is a link that might be useful: Purslane

if you could just give it 6 inches of no mowing ... for a month or two ... you could dig out the bulb and move it to a garden bed ... on such.. you need to let the plant restore energy.. before it goes dormant ... if you dig it now.. maybe you win.. maybe you dont ... but looking at that perfect green carpet .. i doubt you want to let it naturalize.. as flora suggests ... what surprises me.. with your perfect lawn .. is that it seems immune to excessive fert.. and presumably weed agents ... go figure.. tough little bugger ... if you want it moved... take a butcher knife ... cut a cross .. pull back the sod.. so you can dig out the bulb ... go place it in a garden bed ... and reset the sod ... and bobs your uncle ... ken

You could be right! I seem to remember planting something by that name in a planter, last year. It didn't return in the planter but this might be an offspring.