First, let's see what Brahmayajna really is.
According to Manu Smriti 3.70:
अध्यापनं ब्रह्मयज्ञः पितृयज्ञस्तु तर्पणम् ।
होमो दैवो बलिर्भौतो नृयज्ञोऽतिथिपूजनम् ॥ ७० ॥
adhyāpanaṃ brahmayajñaḥ pitṛyajñastu tarpaṇam |
homo daivo balirbhauto nṛyajño'tithipūjanam || 70 ||
Teaching is the ‘offering to Brahma;’ the Tarpaṇa is the ‘offering to Pitṛs;’ the Homa is ‘offering to Gods;’ the Bali is ‘offering to elementals;’ and the honouring of Guests is ‘offering to men.’—(70)
Note that Brahmayajna literally means a sacrifice or offering to Brahma.
According to this, Brahmayajna is the teaching. However, if we look at Medhatithi's commentary on the Manusmriti:
The term ‘teaching’ here includes ‘learning’ also. The mere act of ‘reciting’ does not require any pupils. In the Vedic text describing the ‘debts’ of man, it has been stated in general terms that ‘by means of Vedic study one pays off one’s debts to the sages.’ For these reasons, both ‘teaching’ and ‘learning,’ according to circumstances, constitute ‘the offering to Brahma.’
Now, I'm going to be straightforward here: nowhere in any of the Puranas does it say your father must be deceased.
According to the Shiva Purana, recitation of the Vedas is known to be Brahmayajna. It recommends all Dvijyas to do this.
The regular study of the Vedas is called Brahmayajña. A Dvija shall perform this constantly for the propitiation of gods.
This is to be practised by all viz. only twice-born) and hence no special rules are prescribed here. Now attend to the explanation of certain Devayajñas without fire. (Shiva Purana, Vidyeshvara Samhita, Chapter 14)
The Devi Bhagavatam Purana elucidates the entire procedure for Brahmayajna before reading the Vedas:
1-25. The twice born (Dvija) is firstly to sip three times (make Ācamana); then to make the mārjana (sprinkle water) twice; he is to touch the water by the right hand and sprinkle water on his two feet. Next, he is to sprinkle with water his head, eyes, nose, ears, heart, and head thoroughly. Then speaking out the Deśa and Kāla (place and time) he should commence the Brahmā Yajñā. Next for the destruction of all the sins and for getting liberation, he should have the Darbha (sacrificial grass, and the Kuśa grasses), two on his right hand, three on his left hand, one grass each on his seat, sacrificial thread, his tuft, and his heels. No sin can now remain in his body. (Devi Bhagavatam Purana, Skandha 11, Chapter 20)
The definition of Brahmayajna is asserted in the Garuda Purana:
The performance of a Brahma-yajna consists in teaching the Vedas, that of a Pitri-yajna consists in offering oblations and libations of water to one’s departed manes. (Garuda Purana, Dhanvantari Samhita, Chapter CCXXIX)
Same in the Padma Purana as well:
Teaching and reciting the Vedas (brahmayajña), reception of guests (nṛyajña), sacrifice to the superior gods made by oblations to fire (devayajna), obsequial offerings (pitṛyajña), an oblation to all created beings (bhūtayajña), are said to be the five sacrifices. The wise call this—namo bhagavate Vāsudevāya (Salutation to the revered Vāsudeva) preceded by (the syllable) Om to be a great formula of twelve syllables. O best brāhmaṇa, I have thus told you what was asked by you. (Padma Purana, Kriyayogasara Kandha, Chapter 17)
We now know what a Brahmayajna is. A Brahmayajna is the recitation or optionally impartion of the Vedas (to students if teaching.)
However, you know one thing I did not see? The mention of father anywhere, much less the mention that your father must be deceased in order to perform it.
I think it is self-explanatory to say that you can do this upon your own volition.
I hope this helped!