Question

Answer

I am referring to Rig Vedic mantras alone, which are the oldest and considered to be apaurushEya.

The definition of Sannyasa was already elaborated by the OP. Hence, I am not reproducing similar content here.

The Rig Vedic mantras were composed by the Sages. They prayed, apart from wealth, for children also.

Let us examine a few of them.

Rig Veda II.2.12 - Rishi - Gristamada

उभयासो जातवेदः सयाम ते सतोतारो अग्ने सूरयश्च शर्मणि | वस्वो रायः पुरुश्चन्द्रस्य भूयसः परजावतः सवपत्यस्य शग्धि नः ||

Knower of all that lives, O Agni may we both, singers of praise and chiefs, be in thy keeping still. Help us to wealth exceeding good and glorious, abundant, rich in children and their progeny.

  1. Rig Veda III.8.6 - Rishi - Viswamitra , says

Ye whom religious men have firmly planted; thou Forest Sovran whom the axe hath fashioned,— Let those the Stakes divine which here are standing be fain to grant us wealth with store of children

So the sages of Rig Vedic period did not think that for attaining SPIRITUALITY, marriage and children are hindrance.

Sanyasa might be later day development.

Note: “The question: Is sannyasa a Vedic way of life? Is it recommended by the Vedas, the ten authentic Upanishads or Grhyasutras?” is licensed by Stack Exchange Inc (https://hinduism.stackexchange.com/); user contributions licensed under CC BY-SA.