After this impressive start comes the long haul. To Japan, to be precise, which is Celtic's next stop, for a friendly on Thursday against Yokohama Marinos, before the first real test of their title-retaining credentials at Hearts next weekend.
Gordon Strachan was in a good mood after seeing the 2005-06 championship flag unfurled before kick-off and then watching Kilmarnock unpicked with ease. His side scored four goals, the best a free-kick by Shunsuke Nakamura. They created other chances. And all that while five signings made competitive debuts, three from the start.
"You can't ask for more," Strachan said, "although I know there are people who will. We must be the only club in history to have won the title by 21 points and then be told we're under pressure before the first game of the new season."
Acknowledgement of the positives must come in context. For the record, Celtic took last season's title by 17 points, many won against sides like Killie, who have not won at Celtic for more than 50 years and were never likely to on Saturday.
Celtic's best player - and there were several contenders including Mark Wilson and Aiden McGeady - was Stilian Petrov, a man who wants a transfer to England asap. The Bulgarian pulled the strings in midfield and his departure would be a huge loss.
Less worrying is the ridiculous trip to Japan. "Only Nakamura has to play," said Strachan of Celtic's contractual liabilities. Mostly juniors will travel. "We'll take masks of our big players," he japed.
The new players did well, Kenny Miller linking well promisingly with Maciej Zurawski, who scored twice. Jiri Jarosik was also on target in a composed display. Gary Caldwell looked nervy at first in defence, but these are early days.
Goals: Zurawski (25) 1-0; Jarosik (38) 2-0; Nakamura (75) 3-0; Naismith (87) 3-1; Zurawski (90) 4-1.
Celtic (4-4-2): Boruc; Wilson, Caldwell, McManus, Camara; Nakamura, Petrov, Jarosik (Sno, 84), McGeady; Miller (Riordan, 88), Zurawski. Substitutes not used: Marshall (gk), Thompson, Varga, Lawson, Wallace.
Kilmarnock (4-4-2): Smith; Greer, Lilley, Wright, Hay; Invincible, Johnston, Fowler, Naismith; Nish (Wales, 63), Di Giacomo (Leven, 69). Substitutes not used: Bell (gk), G Murray, O'Leary, Hamill, S Murray.
Referee: I Brines.
Booked: Celtic Boruc; Kilmarnock Greer.
Man of the match: Petrov.
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