The meaning of “without a beginning” (al-‘Awwal), is  the One Who does not have a beginning to His Existence. Allah is the only one Who is eternal in this context. Allah said in Surat al-Hadid verse #3:

﴿هُوَ اْلأَوَّلُ وَاْلآخِرُ﴾ سورة الحديد

The verse means: [Allah is the One Who does not have a beginning and does not have an end to His Existence.]

The Eternal “al-Qadim” has the same meaning as “al-‘Awwal” when referring to Allah.  The nation unanimously agreed on the validity of attributing the name “al-Qadim” to Allah.  Az-Zabidiyy narrated this agreement in his book ‘Sharh Ihya’ ^Ulum id-Din’.