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It's actually possible to use the fact that block-times are locally roughly linearly separated to optimize far beyond a binary search.

This code typically finds the closest block with 3 or 4 calls:

from web3 import Web3, WebsocketProvider

web3 = Web3(WebsocketProvider(f'wss://:{PROJECT_SECRET}@mainnet.infura.io/ws/v3/{PROJECT_ID}'))

import  arrow

T = lambda i_block: web3.eth.getBlock(i_block).timestamp

ilatest = web3.eth.get_block('latest')['number']

def iblock_near(tunix_s, ipre=1, ipost=web3.eth.get_block('latest')['number'], radii=[25000, 1000, 100, 8, 1]):
    ipre = max(1, ipre)
    ipost = min(ilatest, ipost)

    t0, t1 = T(ipre), T(ipost)

    av_block_time = (t1 - t0) / (ipost-ipre)

    print()
    print(f'Searching between blocks {ipre} ({t0}) and {ipost} ({t1})')

    # if block-times were evenly-spaced, get expected block number
    k = (tunix_s - t0) / (t1-t0)
    iexpected = int( ipre + k * (ipost - ipre))

    # get the ACTUAL time for that block
    texpected = T(iexpected)

    off_by_nblocks = abs(int((texpected - tunix_s) / av_block_time))

    print(f'target timestamp ({tunix_s}) lies {k:.3f} of the way from block# {ipre} ({t0}) to block# {ipost} ({t1})')
    print('Expected block#:', iexpected)
    print('Actual timestamp of expected block:', texpected)
    print('Off by', off_by_nblocks, 'blocks')

    if off_by_nblocks == 0:
        print('GOT IT')
    else:
        return iblock_near(tunix_s, iexpected - off_by_nblocks, iexpected + off_by_nblocks)

tunix_s = arrow.get('2018-06-11T12:34:56').timestamp()
block = iblock_near(tunix_s)

Output: