Hives, Birrell, Sharma and Hon are among 14 Australians in action on day one.
"I'm very happy with my performance today", the 19-year-old said after the win on Margaret Court Arena. "I think they are punishing Aussies for playing deep in their home tournaments and I think that's not what they should be doing".
He also had to contend with stifling hot conditions in Melbourne, with the mercury reaching 34 degrees as he and Sousa took to the court.
"If you see me driving, you might want to watch out", de Minaur said with an ear-to-ear grin.
De Minaur, the 2018 ATP newcomer of the year, still had a break of serve up his sleeve and it proved enough security for him to finish off his opponent in just under two hours.
He will face either Mirza Basic or Henri Laaksonen in the second round, with a potential third-round meeting with world number two Rafael Nadal on the horizon.
Sharma prevailed against countrywoman Priscilla Ho 7-5, 4-6, 6-1 in an enthralling contest on the outside courts lasting two hours and nine minutes.
Barty also insisted she'd enter this year's tournament better placed and as a better player than the one who was knocked out last year in the third round.
She more than doubled her prize money courtesy of the win over the wildcard Ho, earning $85,000, and it is just reward after she took a punt on a USA college scholarship to Vanderbilt University in Nashville after sustaining a broken ankle early in her career. I feel like I'm a much better player. Fitness-wise, I felt like I could keep going, as well'. If both progress as they hope, the would meet in quarter final.
Hives defied her world ranking of No 225 to upstage seasoned American Bethanie Mattek-Sands 6-1, 6-2 before Birrell joined her in the second round with a 6-4, 6-2 defeat of Spanish qualifier Paula Badosa Gibert.