我早上七点半就出门了 Means I left home at a quite early time 7:30am (quite early for the schedule) 我早上八点半才出门 Means I left home at 8:30am which is considered a bit late for the schedule

Grammar: Time+就/才+Verb “就” often indicates the time Is short or early. On the contrary, “才”, usually speaking of long time or late time. This judgment about the time is based on the speaker's subjective ideas. E.g, 我家离公司很近，走路十分钟就到了。 他家离公司很远，开车半小时才到。 他今天早上五点就出门了。晚上八点才回家。

八点半就出门了is telling the fact. and八点半才出门 means I left home very late

"就”means that you think you go out early, and "才”means that you think you go out late

在您提供的语境中“就”和“才”分别表示： 1、“就” 表达出门这个动作发生的时间比预定或预期早，常有出人意料的意味。 例如：会议八点开始，他七点半就来了。 2、“才” 表达动作发生的时间比预想的时间晚。 例如：会议八点开始，他八点半才到。