UUIDv7 on PostgreSQL without Extension. I recommend using pgcrypto's gen_random_bytes instead of random.

select_uuidv7.sql

-- Copyright 2025 taichi
-- 
-- Licensed under the Apache License, Version 2.0 (the "License");
-- you may not use this file except in compliance with the License.
-- You may obtain a copy of the License at
-- 
--     http://www.apache.org/licenses/LICENSE-2.0
-- 
-- Unless required by applicable law or agreed to in writing, software
-- distributed under the License is distributed on an "AS IS" BASIS,
-- WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-- See the License for the specific language governing permissions and
-- limitations under the License.
SELECT encode(
  int8send(((extract(epoch from current_timestamp) * 1000)::bigint << 16) | (0x7::bigint << 12) | (floor((EXTRACT(MICROSECONDS FROM current_timestamp) % 1000) / 1000.0 * 4096)::bigint)) || -- msb
  int8send((0x2::bigint << 62) | ((random() * 0x3FFFFFFF)::bigint << 32) | ((random() * 0xFFFFFFFF)::bigint)) -- lsb
, 'hex')::uuid;

uuid_generate_v7.sql

-- Copyright 2025 taichi
-- 
-- Licensed under the Apache License, Version 2.0 (the "License");
-- you may not use this file except in compliance with the License.
-- You may obtain a copy of the License at
-- 
--     http://www.apache.org/licenses/LICENSE-2.0
-- 
-- Unless required by applicable law or agreed to in writing, software
-- distributed under the License is distributed on an "AS IS" BASIS,
-- WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-- See the License for the specific language governing permissions and
-- limitations under the License.

-- UUIDv7 generation
-- https://www.rfc-editor.org/rfc/rfc9562.html
CREATE OR REPLACE FUNCTION uuid_generate_v7() RETURNS uuid
    LANGUAGE plpgsql
AS $$
DECLARE
    ts timestamptz;
    unix_ts_milli bigint;
    unix_ts_micro bigint;
    msb bigint;  -- most significant bits
    lsb bigint;  -- least significant bits
BEGIN
    ts := clock_timestamp();
    unix_ts_milli := (extract(epoch from ts) * 1000)::bigint;
    unix_ts_micro := floor((EXTRACT(MICROSECONDS FROM ts) % 1000) / 1000.0 * 4096)::bigint;

    -- [unix_ts_ms(48bits) | version(4bits) | rand_a(12bits)]
    msb := (unix_ts_milli << 16) |  -- unix_ts_ms
           (0x7::bigint << 12) |    -- Version 7
           unix_ts_micro;           -- Method 3

    -- [variant(2bits) | rand_b(62bits)]
    lsb := (0x2::bigint << 62) | -- 0b10
           ((random() * 0x3FFFFFFF)::bigint << 32) |
           ((random() * 0xFFFFFFFF)::bigint);

    RETURN encode(int8send(msb) || int8send(lsb), 'hex')::uuid;
END;
$$;