Join one table to another based on certain conditions met by rows in second table

I have two tables. I want to create a SQL query such that for each row in Table 1, I want find the first two rows in Table 2 such ms.Table2 > ms.Table1. The resulting output will be Table 1 with six additional columns added showing ms, bid, ask from Table 2 corresponding to first two rows from Table 2 where ms is just greater than ms in Table 1.

Given the large number of rows, doing a cross-join and then filtering may be too much (since this has to be done many times over multiple data, not just once). Looking for an efficient solution. I am new to SQL so feel this is bit much for me, though I did try a cross-join. Please help!

Table 1 (2000+ rows)

Table 2 (300000+ rows)

you could use a loop, but it will still be somewhat slow, but much faster than a cross join

CREATE TABLE table1
("ms" int, "price" int, "bid" int, "ask" int)
;
INSERT INTO table1
("ms", "price", "bid", "ask")
VALUES
(34200106, 1.48, 1.46, 1.5),
(34200106, 1.48, 1.46, 1.5),
(34202812, 1.56, 1.53, 1.56),
(34202815, 1.56, 1.53, 1.56),
(34202823, 1.56, 1.53, 1.56),
(34204227, 1.56, 1.53, 1.57),
(34207137, 1.56, 1.55, 1.57),
(34208496, 1.57, 1.56, 1.57),
(34208938, 1.57, 1.55, 1.57),
(34208938, 1.57, 1.55, 1.57),
(34208943, 1.57, 1.55, 1.57),
(34208951, 1.57, 1.56, 1.57)
;

> status
> CREATE TABLE
>

> status
> INSERT 0 12
>

CREATE TABLE table2
("ms" int, "bid" int, "ask" int)
;
INSERT INTO table2
("ms", "bid", "ask")
VALUES
(34200009, 1.46, 1.51),
(34200011, 1.46, 1.5),
(34200106, 1.46, 1.5),
(34200171, 1.46, 1.5),
(34200195, 1.46, 1.5),
(34200195, 1.46, 1.51),
(34200201, 1.46, 1.52),
(34200202, 1.46, 1.52),
(34200276, 1.46, 1.52),
(34200296, 1.46, 1.52),
(34200305, 1.46, 1.52),
(34200306, 1.46, 1.52),
(34200308, 1.46, 1.53),
(34200326, 1.46, 1.53)
;

> status
> CREATE TABLE
>

> status
> INSERT 0 14
>

CREATE OR REPLACE FUNCTION foo() 
RETURNS TABLE ("ms" int, "price" int, "bid" int, "ask" int)
language plpgsql as $$
DECLARE 
x int ;
table1_cursor CURSOR FOR SELECT t1."ms" FROM table1 t1; 
BEGIN
CREATE TEMP TABLE IF NOT EXISTS temp_table AS
SELECT *
FROM table1;
FOR x IN table1_cursor loop
INSERT INTO temp_table ("ms", "price", "bid", "ask")
SELECT t2."ms", NULL, t2."bid", t2."ask" FROM table2 t2
WHERE t2."ms" > x."ms"
ORDER BY t2."ms" 
LIMIT 2;
END loop;
RETURN QUERY 
SELECT t3."ms", t3."price", t3."bid", t3."ask"
from temp_table t3;
DROP TABLE temp_table;
END $$;
SELECT * FROM foo();

> status
> CREATE FUNCTION
>

fiddle

The following query produces the described results without doing a full cross join between table1 and table2:

SELECT table1.ms,
table1.bid,
table1.ask,
t2.ms[1] AS ms1,
t2.bids[1] AS bid1,
t2.asks[1] AS ask1,
t2.ms[2] AS ms2,
t2.bids[2] AS bid2,
t2.asks[2] AS ask2
FROM table1
CROSS JOIN LATERAL (SELECT ARRAY_AGG(t.ms) AS ms,
ARRAY_AGG(t.bid) AS bids,
ARRAY_AGG(t.ask) AS asks
FROM (SELECT table2.*
FROM table2
WHERE table2.ms > table1.ms
ORDER BY table2.ms
LIMIT 2
) t
) AS t2;