Are the first solo flights by a student pilot more dangerous?
There is no evidence to back the claim that the first solo ride of the student is more dangerous compared to the later ones.
US NIH conducted a study on the accidents with solo pilots, which doesn't indicate that first-time solo fliers are any more prone to accident than others. Aircraft accidents with student pilots flying solo: analysis of 390 cases by  Sjir Uitdewilligen and Alexander Johan de Voogt analyzed NTSB probable cause reports of 390 crashes that occurred in the period 2001 – 2005, concluding that,

Student pilots flying solo show fewer injuries and fatalities compared to general instructional flights while in our sample first-time solo student pilots did not feature any fatalities.

Note that this gives only the injuries and not the times the students got into accidents per se. Out of a total of 3811 accidents involving student pilots, 390 occurred while they were flying solo and around 50 involved first-time student solo pilots. Actually, student pilots themselves are prone to less accidents compared to others. From Comparative Analysis of Accident and Non-Accident Pilots by David C. Ison:

Most accidents (49.1%) were conducted with individuals holding a private pilot certificate. Second in incidence were commercial pilots (28.2%), followed by Airline Transport Pilots (ATPs) (13.7%), and student pilots (5.7%)
Considering that 20% of pilots hold a student certificate, these individuals have a disproportionally low accident occurrence.

The report also gives some additional insight into the reason the first-time solo fliers have lesser injuries:

... first-time solo pilots are commonly confined to the airport and practice their takeoff and landings. Such operations may result in accidents, but they will occur near to the ground with a lower risk of a fatality

The report also gives some data about higher experienced student pilots sustaining more injuries, though nothing conclusive, noting that,

... in 25 cases, student pilots were reported to have more than 100 and up to 322 h of flight experience. In the dataset, these pilots were significantly more often injured than students with less hours of flight experience.

It has to be noted that as the hours logged gets more, the students get into more demanding flights which may be reason for this increase in injuries.