Skipping a fast during Ramadan (with the excuse of travelling) is only allowed for someone whose journey begins before subah sadiq (the break of dawn). In the situation described in the question, the person intends to begin their journey in the afternoon rather than before subah sadiq. Therefore, it is not permissible for them to skip that day's fast.
A relaxation provided by Shariah in this case is that if the person ends up breaking their fast before sunset after having travelled a distance far enough to be considered "safar" according to Shariah, then kaffarah will not become obligatory. The person must only perform qaza for the missed fast.
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دلائل:
الھندیة: (الباب الخامس في الإعذار التي تبیح الإفطار، 269/1، ط: اتحاد، دیوبند)
منہا السفر الذي یبیح الفطر، وہو لیس بعذر في الیوم الذي أنشأ السفر فیہ، کذا في الیاثیة، فلو سافر نہارًا، لا یباح لہ الفطر في ذلک الیوم وإن أفطر لا کفارة علیہ بخلاف ما لو أفطر، ثم سافر کذا في محیط السرخسي
Allah the Almighty knows best,
Darul ifta Al-Ikhlas, Karachi.