Dear Jigar Shah Ji,
I agree with Sh Alkesh Jani Ji. But you have other options too. Registration as 'Casual Taxable Person' is one of the options. Pl note that it is optional and not mandatory. In this scenario, registration as a casual taxable person may not be useful for A. Further my views are as under :-
1. First of all go through the definitions of 'Place of business', "Location of supplier of service', 'Fixed establishment'
2. In terms of Section 22 (1) of CGST Act, registration is required only from where taxable supply is made' and NOT where taxable is made'.
3. A perusal of query indicates that A has no fixed establishment in Goa. A temporary place cannot be 'location of supplier of service'.
4. A can be covered under Section 2(15) of IGST Act under clause (a) and (d) of the definition of 'Location of supplier of service'.
5. A's Place of business can be in terms of Section 2(85) (b) of CGST Act read with definition of 'location of supplier of service'
6. Registration in other State (Goa) is required only at a place where supplier of service or goods has fixed establishment.
Q No.1 Can the company A take Input credit of IGST from bill raised by company B (Sub-contractor) ? Are there any issues if company B raised bill for material and service purchase and used in Goa to Company A in Ahmedabad?
Ans. ITC can be taken provided that conditions mentioned in Section 17(5) (c) &(d) are qualified for. No problem as C is A's customer.
Q. No.2 And Also Issue is that Company A not having registered office in Goa, can it raise invoice to Company C for work done in Goa ?
Ans. Yes. A can raise invoice in the name of C. C is A's customer.
Also go through the following :-
1. AAR, Karnataka's decision dated 31.3.20 reported as 2020 (36) GSTL 239 (AAR-GST Kar = 2020 (4) TMI 693 - AUTHORITY FOR ADVANCE RULING, KARNATAKA in the case of T & D Electricals.
2. Board's Flyer No.28 dated 1.1.18 Para No.6 under the Head-'Position under GST'
3. Tweet FAQ dated 26.6.17 (serial No.61).
If a huge amount of ITC of inputs and services is to be received in Goa, better option is to register in Goa.
Thus A has both options.