No. The Manusmṛti is not meant for our time, nor theirs.
I alluded to it not being our time before, however, I didn't say when it is meant to be for, because it never came up.
First of all, it can't be our time because:
सरस्वतीदृशद्वत्योर्देवनद्योर्यदन्तरम् ।
तं देवनिर्मितं देशं ब्रह्मावर्तं प्रचक्षते ॥ १७ ॥
sarasvatīdṛśadvatyordevanadyoryadantaram |
taṃ devanirmitaṃ deśaṃ brahmāvartaṃ pracakṣate || 17 ||
The region lying between the divine rivers Sarasvati and Dṛṣasvatī which has >been created by the gods,—they call ‘Brahmāvarta’—(17)
Thus, the Sarasvatī river is clearly flowing and is used as a location marker
There are other hints like:
विद्या शिल्पं भृतिः सेवा गोरक्ष्यं विपणिः कृषिः ।
धृतिर्भैक्षं कुसीदं च दश जीवनहेतवः ॥ ११६ ॥
vidyā śilpaṃ bhṛtiḥ sevā gorakṣyaṃ vipaṇiḥ kṛṣiḥ |
dhṛtirbhaikṣaṃ kusīdaṃ ca daśa jīvanahetavaḥ || 116 ||
Learning, handicrafts, working on hire, service, cattle-tending, trade, agriculture, >contentment, begging and money-lending,—these are the ten means of livelihood.—(116)
There are a few hints in the Manusmṛti that food is free in this world (at least enough to live on). Contentment being a method of livelihood is one of the most blatant. (As a side note the literal interpretation of a verse in the same chapter as this implies a Śūdra can become a Brāhmaṇa by serving one, without having to be reborn)
षट् त्रिंशदाब्दिकं चर्यं गुरौ त्रैवेदिकं व्रतम् ।
तदर्धिकं पादिकं वा ग्रहणान्तिकमेव वा ॥ १ ॥
ṣaṭ triṃśadābdikaṃ caryaṃ gurau traivedikaṃ vratam |
tadardhikaṃ pādikaṃ vā grahaṇāntikameva vā || 1 ||
Duties relating to the Three Vedas should be observed under the Preceptor for thirty-six >years, or for half that period, or for a quarter, or precisely till they have been got >up.—(1)
This study period, which can be up to 36 years, is way too long (for one subject) to be practical for our lifespans.
Anyway, the actual timespan the Manusmṛti is given for is actually easily determinable from the fact there are seven Manus and the following verses:
शनकैस्तु क्रियालोपादिमाः क्षत्रियजातयः ।
वृषलत्वं गता लोके ब्राह्मणादर्शनेन च ॥ ४३ ॥
śanakaistu kriyālopādimāḥ kṣatriyajātayaḥ |
vṛṣalatvaṃ gatā loke brāhmaṇādarśanena ca || 43 ||
But by the omission of the sacred rites, and also by their neglect of Brāhmaṇas, the >following Kṣatriya castes have gradually sunk to the position of the low-born.—(43)
पौण्ड्रकाश्चौड्रद्रविडाः काम्बोजा यवनाः शकाः ।
पारदापह्लवाश्चीनाः किराता दरदाः खशाः ॥ ४४ ॥
pauṇḍrakāścauḍradraviḍāḥ kāmbojā yavanāḥ śakāḥ |
pāradāpahlavāścīnāḥ kirātā daradāḥ khaśāḥ || 44 ||
The Puṇḍrakas, the Coḍas, the Draviḍas, the Kāmbojas, the Yavanas, the Śākas, the >Pāradas, the Pahlavas, the Cīnas, the Kirātas, the Daradas and the Khaśas.—(44)
The events above are described in other scriptures and are very close to the modern day. Combining with there being seven Manus implies:
The Manusmṛti applies to a time in the future of this Manvantara we are in
https://www.wisdomlib.org/hinduism/book/manusmriti-with-the-commentary-of-medhatithi/d/doc145593.html
https://www.wisdomlib.org/hinduism/book/manusmriti-with-the-commentary-of-medhatithi/d/doc201858.html
https://www.wisdomlib.org/hinduism/book/manusmriti-with-the-commentary-of-medhatithi/d/doc199771.html
https://www.wisdomlib.org/hinduism/book/manusmriti-with-the-commentary-of-medhatithi/d/doc201774.html